# Probability calculation sheet

More About the F-distribution. The F-distribution is one of the most fundamental distributions in Statistics, along with the normal distribution and the Chi-Square distribution. Technically, the F-distribution is obtained by constructing the ratio between two properly scaled variables that have a Chi-Squared distribution. Indeed if. U 1. U_1 U 1.Probability: Review Sheet An example The binomial coefficient can also be used to calculate the chance of an event occurring a certain number of times in a sequence of events. For example, the chance that a die is tossed five times and exactly three of the tosses turn out to be 4: "5 choose 3" multiplied by three times and two times.Probability Calculator. For dependent events enter 3 values. For independent events input 2 values. show help ↓↓ examples ↓↓. I want to calculate: Input values you know. P ( A ) =. P ( B ) The probability is 5 ÷ 20 = 1/4. You could also express this as 0.25 or 25%. 4 Add up all possible event likelihoods to make sure they equal 1. The likelihood of all possible events needs to add up to 1 or to 100%.Probability and statistics. Here is a list of all of the skills that cover probability and statistics! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as ... When two events are independent, you can use the following formula. probability (A and B) = probability (A) × probability (B) Let's use this formula to find the probability of getting 2 heads when two coins are tossed. probability (H and H) = probability (H) × probability (H) Coin #1: Probability of getting head =. 1 2.Decide by calculation how many candidates out of a total of 1000 candidates for the position of CEO meet the eligibility requirements for the desired performance of this top management position with at least 67% probability - provided, of course, that the; SD - mean The mean is 10 and the standard deviation is 3.5.For the serial compound availability multiply the probability of each component being available: So: 99.95% * 99.95% = 0,99900025% = 99.9%. Calculating it in parallel is a little more complicated as we do need to consider what the percentage unavailability will be: The calculation is done as follows:Probability tree diagrams are used to calculate probabilities for both dependent and independent events. A probability tree diagram shows all the possible events. The first event is represented by a dot. The probability is written on its branch. Probability tree diagrams Worksheet helps students practice this tool for calculating probabilities.Given a set of values and corresponding probabilities, calculates the probability that a value chosen at random falls between two limits. Sample Usage PROB({1,2,3,4},{0.25,0.25,0.25,0.25},3) PROB(A. ... low_limit - The lower bound on the value range for which to calculate the probability. high_limit - [OPTIONAL - low_limit by default ] ...Odds. The odds in favor of an event is the ratio of the number of ways the outcome can occur to the number of ways the outcome cannot occur. # of ways the event CAN occur : # of ways the event CANNOT occur. This is actually a lot easier than probability. So, let's take a look at an example. Using multiplication, we can calculate (1) the number of possible allele combinations for a given cross, and (2) the probability of an offspring having a particular allele combination. 1. First, we’ll apply math to the sex chromosome example. Here’s the math for calculating the number of possible combinations: Solution: If using a calculator, you can enter λ = 3.3 λ = 3.3 and x = 5 x = 5 into a poisson probability distribution function (PDF). If doing this by hand, apply the poisson probability formula: P (x) = e−λ ⋅ λx x! P ( x) = e − λ ⋅ λ x x! where x x is the number of occurrences, λ λ is the mean number of occurrences, and e e is ...P (E) = n (E) / n (S) This reads as follows: The probability of an event occurring is equal to the number of occurrences of an event divided by the total number of possible outcomes. Let's take a look at a quick scenario where we can use the PROB function to calculate probabilities.This applet computes probabilities and percentiles for the exponential distribution: X ∼ e x p ( λ) It also can plot the likelihood, log-likelihood, asymptotic CI for λ, and determine the MLE and observed Fisher information. Parameterization. f ( x) = λ e − λ x for x > 0 (and 0 otherwise) E ( X) = 1 / λ. V a r ( X) = 1 / λ 2.Rummy game free download!! poker probability calculator Download Indian rummy for free on KhelPlay Rummy.com. Visit this page to download 13 card rummy game baccarat game (free download for android). RG CREATIONS YT This is the section where you can find the Probability Formulas list. Have a glance at the list before you start computing probability calculations. If you memorize these Probability Formulas daily then you can simplify all probability problems easily & effortlessly. 1. Definitions (i) Trial and Event:Entering the X² sum of 23.8872 and the degrees of freedom (32, one less than the 33 possible outcomes of the experiment) into the Chi-Square Calculator gives a probability of 0.85. This falls within the "fat region" of the probability curve, and thus supports the null hypothesis, just as we expected. Next, we invite our subject to attempt to influence the random output of our generator.Using Probability. 7th Grade Math Worksheets and Answer key, Study Guides. Covers the following skills: Understand and apply basic concepts of probability. Probability word problems worksheet. Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models. Homework. U.S. National Standards. Probability and statistics. Here is a list of all of the skills that cover probability and statistics! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as ... Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.Enter data in Excel sheet. 2. To calculate probability, use the PROB function. The formula here is =PROB (A2:A10,B2:B10,B13,B14) where. A2:A10 is range of marks in this example. B2:B10 is a chance of getting the grade from A column. B13 is lower range. B14 stand for upper range. The probability here is 45%.Option Chain probability can help you earn huge profit from the stock market. However, the option chain analysis helps investor or trader to find out the sho...Students must identify the probability for selecting the candy, most probable selection, least probable, etc. Each worksheet has 12 problems covering spinner wheels, dice and arrays of objects. Each worksheet has 12 problems examining the most probable, least probable or equally probable chance of landing on a section. Enter data in Excel sheet. 2. To calculate probability, use the PROB function. The formula here is =PROB (A2:A10,B2:B10,B13,B14) where. A2:A10 is range of marks in this example. B2:B10 is a chance of getting the grade from A column. B13 is lower range. B14 stand for upper range. The probability here is 45%.Whether you want to calculate probability in fractions or percentages, you will need the total number of possible outcomes in the sample space, and the total number desired outcomes. You need to divide the total number of possible outcomes by the total number of desired outcomes. To calculate the probability in the percentage, you can then ...P (AKKQJ) =. 768. 311875200. Probability (Choose Your Hand) =. 768. 311,875,200. Using our GCF Calculator, we see that 768 and 311875200 can be reduced by 384. Reducing top and bottom by 384, we get: Probability (Choose Your Hand) =. Basic Probabilities Excel Calculator. Students often are given questions that require them to find basic and conditional probabilities for a 2×2 matrix such as this problem: You can work this problem using StatCrunch using the Stat>Tables>Contingency path, but some students get confused by the cluttered output. I have developed an Excel ...Problems on statistics and probability are presented. The answers to these problems are at the bottom of the page. Given the data set. 4 , 10 , 7 , 7 , 6 , 9 , 3 , 8 , 9. Find. a) the mode, b) the median, c) the mean, d) the sample standard deviation. We can use the formula to find the chances of an event happening. Formula to Calculate Probability The formula of the probability of an event is: Probability Formula Or, P (A) = n (A)/n (S) Where, P (A) is the probability of an event “A” n (A) is the number of favourable outcomes n (S) is the total number of events in the sample space Intuitively, it's difficult to estimate the most likely success, but with our dice probability calculator, it takes only a blink of an eye to evaluate all the probabilities. The resulting values are: P₁ = 0.38125 for 10 sided dice. P₂ = 0.3072 for 12 sided dice. P₃ = 0.3256 for 20 sided dice.Jonathan spins 2 spinners; one of which is labeled 1, 2 and 3, and the other is labeled A, B, C and D. Given that all the outcomes are equally likely, find the probability that: a) the spinners stop at "2" and "C". b) the spinners stop at "3" and either "B" or "D". c) the spinners stop at "A" and any number. Albert ...84 Activity Central. Download free activities that enhance your lesson plans and enable students to visualize mathematics in middle grades through high school topics. Select a Subject. Jun 29, 2020 · This grade 10 math literacy worksheet on probability covers all the basics. Topics include. theory and definitions of words. expressions of probability. terms. probability scale. relative frequency vs theoretical probability. two-way tables. tree diagrams. Theoretical Probability Worksheet 2 - Here is a fourteen problem worksheet where you will calculate the theoretical probability of an event. You will determine the total number of outcomes in each situation, then decide how many of those outcomes match your desired outcome. Finally, you will express the probability as a number between 0 and 1.Statistics and probability. There are 7 calculators in this category . Descriptive Statistics Calculator - Find Arithmetic mean, mode, median, minimum, maximum of a data set. Standard Deviation Calculator - Find standard deviation, variance and range of a data set. Probability Calculator - Finds conditional probability, union and intersection of events. ...Data ( US: / ˈdætə /; UK: / ˈdeɪtə /) are individual facts, statistics, or items of information, often numeric.  In a more technical sense, data are a set of values of qualitative or quantitative variables about one or more persons or objects,  while a datum (singular of data) is a single value of a single variable.  Probability calculator is free and easy to use. You just need to follow below steps. Step #1: Define the probabilities of single or multiple events you want to calculate. Probabilities must have two separate events. Probability of A: P (A) and. Probability of B: P (B) Step #2: Find the Probability of an event.Calculate Binomial Distribution in Excel. The BINOM.DIST function is categorized under Excel Statistical functions. It calculates the binomial distribution probability for the number of successes from a specified number of trials. This binomial distribution Excel guide will show you how to use the function, step by step.Statistical Analysis and Probability x = sample mean n = size of the sample s = sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population) o = observed results e = expected results Degrees of freedom are equal to the number of distinct possible outcomes minus one. Mean Standard Deviation* x n x i i n ...This math worksheet introduces your child to probability and reading tables. Share on Pinterest. Parenting » Worksheets » Probability (2nd grade, 3rd grade) Math Probability (2nd grade, 3rd grade) Which kind of marble is least likely to be picked? This math worksheet introduces your child to probability and reading tables.The probability that he will pass at any future attempt is 5. (i) Draw a tree diagram to show the probabilities of Winston passing or failing on each of his first three attempts. (ii) Calculate the probability that he will pass at his third attempt. (iii) Calculate the probability that he wili not need more than three attempts to pass.  [31 For mutually exclusive events: P (A or B) = P (A) + P (B) If we have an exhaustive list of outcomes, their probabilities sum to 1. 1. For example, the probability of getting an even or an odd number on a die. The probability of getting an even number is \frac {3} {6} 63. and the probability of getting an odd number is \frac {3} {6}.Here's a simple example: What's the probability of getting a 6 when you roll a dice? Examine the factors. A dice is a cube with 6 sides, and 1 side contains the number 6. This gives us 1 favorable outcome over a total of 6 possible outcomes. Probability of an event = 1/6 = 0.1666666666666667. The calculation shows the probability is low.This worksheet topic has multiple variations: Calculate the Probability. Find the Probability. Probability on Markers. Probability on Coins. Download All + Answer Keys View All. See Answer Key Print Worksheet.Option Chain probability can help you earn huge profit from the stock market. However, the option chain analysis helps investor or trader to find out the sho...Option Chain probability can help you earn huge profit from the stock market. However, the option chain analysis helps investor or trader to find out the sho...Table 1: The Probability Distribution Functions in R. Table 1 shows the clear structure of the distribution functions. The names of the functions always contain a d, p, q, or r in front, followed by the name of the probability distribution. Hereby, d stands for the PDF, p stands for the CDF, q stands for the quantile functions, and r stands for ...A spinner has three unequal sections: red, yellow, and blue. The table shows the results of Nolan's spins. Find the experimental probability of landing on each color. Solution : Step 1 : Find the total no. of trials. Total number of trials = 10 + 14 + 6 = 30. Step 2 : Find probability for each color.CIS 391- Intro to AI 8 Conditional Probability P(cavity)=0.1 and P(cavity toothache)=0.04 are both prior (unconditional) probabilities Once the agent has new evidence concerning a previously unknown random variable, e.g. Toothache, we can specify a posterior (conditional) probability e.g. P(cavity | Toothache=true) P(a | b) = P(a b)/P(b) [Probability of a with the Universe restricted to b]P (B) = Probability of event B. The following steps outline how to calculate the probability of multiple events: 1. Determine each event you will calculate. The first step for calculating the probability of multiple events occurring at the same time is to determine each of the events you want to work with.Probability Calculator. For dependent events enter 3 values. For independent events input 2 values. show help ↓↓ examples ↓↓. I want to calculate: Input values you know. P ( A ) =. P ( B )Probability on numbers - 1. Probability on numbers - 2. Probability on numbers - 3. Probability on numbers - 4. Probability on numbers - 5. Probability on Deck of Cards. Deck of cards contain 52 cards, 26 are black, 26 are red, four different flowers, each flower contain 13 cards such as A, 1, 2, ..., 10, J, Q, K. Deck of cards worksheet - 1Convert bookmakers odds into probablities with our Odds to Probability Calculator. Put in odds and find margin, fair odds and probability. ... Now, we have West Brom keeping a clean sheet with the probability of 13.49 % and conceding with the probability of 86.51 %. And sum of both probabilities is 100 %.Intuitively, it's difficult to estimate the most likely success, but with our dice probability calculator, it takes only a blink of an eye to evaluate all the probabilities. The resulting values are: P₁ = 0.38125 for 10 sided dice. P₂ = 0.3072 for 12 sided dice. P₃ = 0.3256 for 20 sided dice.Probability and statistics. Here is a list of all of the skills that cover probability and statistics! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as ... Probability Practice Test Question Answers. 1. The probability of getting a number greater than 2 on throwing a die once is. 2. The cards bearing letters of the word "MATHEMATICS" are placed in a bag. A card is taken out from the bag without looking into the bag (at random).If a z-score calculation yields a negative standardized score refer to the 1st table, when positive used the 2nd table. For George's example we need to use the 2nd table as his test result corresponds to a positive z-score of 0.67. Finding a corresponding probability is fairly easy. Find the first two digits on the y axis (0.6 in our example).Using Probability. 7th Grade Math Worksheets and Answer key, Study Guides. Covers the following skills: Understand and apply basic concepts of probability. Probability word problems worksheet. Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models. Homework. U.S. National Standards.We hope your visit to math.com brings you a greater love of mathematics, both for its beauty and its power to help solve everyday problems. Einstein, Albert (1879-1955) Do not worry about your difficulties in mathematics, I assure you that mine are greater. Dirac, Paul Adrien Maurice (1902-1984) I have modified the sheet to include calculate the greeks for NSE stock options. I have combined OI and Greeks analysis for stock options on NSE. The expiry date is auto calculated as the last thursday of current month. The stock option to be analysed must be selected on first sheet from drop down list.Here's a simple example: What's the probability of getting a 6 when you roll a dice? Examine the factors. A dice is a cube with 6 sides, and 1 side contains the number 6. This gives us 1 favorable outcome over a total of 6 possible outcomes. Probability of an event = 1/6 = 0.1666666666666667. The calculation shows the probability is low.Statistics and probability. There are 7 calculators in this category . Descriptive Statistics Calculator - Find Arithmetic mean, mode, median, minimum, maximum of a data set. Standard Deviation Calculator - Find standard deviation, variance and range of a data set. Probability Calculator - Finds conditional probability, union and intersection of events. ...Worksheet A3 : Single Event Probability One of these names is to be drawn from a hat. Determine each probability below: Mary Jenny Bob [Warilyn Bill Jack Jerry Tina Connie Joe (What is the probability of drawing a 3-letter -name?) 3. P(name starting with B) : 5. P(7-letter name) (0 7. P(name ending with Y): (O la P(3-letter name) 10 5 q- 2. Rummy game free download!! poker probability calculator Download Indian rummy for free on KhelPlay Rummy.com. Visit this page to download 13 card rummy game baccarat game (free download for android). RG CREATIONS YT Installation. Download the file Probability Distribution Calculator.opx. Then drag-and-drop the file onto the Origin workspace. An app icon will appear in the Apps Gallery panel. Operation. 1. With a worksheet activate, click the icon from Apps Gallery panel to launch the dialog. 2. Using multiplication, we can calculate (1) the number of possible allele combinations for a given cross, and (2) the probability of an offspring having a particular allele combination. 1. First, we’ll apply math to the sex chromosome example. Here’s the math for calculating the number of possible combinations: Given a set of values and corresponding probabilities, calculates the probability that a value chosen at random falls between two limits. Sample Usage PROB({1,2,3,4},{0.25,0.25,0.25,0.25},3) PROB(A. ... low_limit - The lower bound on the value range for which to calculate the probability. high_limit - [OPTIONAL - low_limit by default ] ...Odds. The odds in favor of an event is the ratio of the number of ways the outcome can occur to the number of ways the outcome cannot occur. # of ways the event CAN occur : # of ways the event CANNOT occur. This is actually a lot easier than probability. So, let's take a look at an example.Probability. How likely something is to happen. Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability. Tossing a Coin. When a coin is tossed, there are two possible outcomes: heads (H) or ; tails (T) We say that the probability of the coin landing H is ½Table 1: The Probability Distribution Functions in R. Table 1 shows the clear structure of the distribution functions. The names of the functions always contain a d, p, q, or r in front, followed by the name of the probability distribution. Hereby, d stands for the PDF, p stands for the CDF, q stands for the quantile functions, and r stands for ...The calculation of probability is initiated with the determination of an event. Every event has two possible outcomes. The first scenario is that it would take place and the second is that it would not. Total outcomes represent the maximum possible results that can be produced. For example, the total outcomes for a day of the week would be 7.Probability calculator is free and easy to use. You just need to follow below steps. Step #1: Define the probabilities of single or multiple events you want to calculate. Probabilities must have two separate events. Probability of A: P (A) and. Probability of B: P (B) Step #2: Find the Probability of an event.Solution: If using a calculator, you can enter λ = 3.3 λ = 3.3 and x = 5 x = 5 into a poisson probability distribution function (PDF). If doing this by hand, apply the poisson probability formula: P (x) = e−λ ⋅ λx x! P ( x) = e − λ ⋅ λ x x! where x x is the number of occurrences, λ λ is the mean number of occurrences, and e e is ...This page contains all our printable worksheets in section Data, Graphs, Probability, and Statistics of Second Grade Math. As you scroll down, you will see many worksheets for tables and tally tables, pictographs, read and make a bar graph, line plots, locate points on a grid, certain, possible, or impossible, more, less or equally likely ... Data ( US: / ˈdætə /; UK: / ˈdeɪtə /) are individual facts, statistics, or items of information, often numeric.  In a more technical sense, data are a set of values of qualitative or quantitative variables about one or more persons or objects,  while a datum (singular of data) is a single value of a single variable.  It's just a factorial. How to calculate the factorial? The simplest thing. Take a number under the factorial sign, a nd multiply it by all the previous numbers to it, except for zero. For example, 3!=3 × 2 × 1=6 3! = 3× 2×1 = 6 . Factorial from 4 4 is considered as the 4 × 3 × 2 × 1 4×3× 2×1, that is 24 24. And so on.Step 1: Show the coin to the class and ask what is the probability of the coin landing on heads. Step 2: Recall the work done in the Make Sense of Basic Probability lesson plan on tree diagrams and ask for a volunteer to explain how all the outcomes for three flips in a row could be depicted. Step 3: Ask what the probability of a coin landing ...Needed to calculate the probability of rolling X amount of successes with Y amount of dice. Great tool.  2019/04/20 17:18 Under 20 years old / High-school/ University/ Grad student / Very / Purpose of use to help with mathWhat are the chances to find the man of your dreams? - Live search on US survey data.Calculate Binomial Distribution in Excel. The BINOM.DIST function is categorized under Excel Statistical functions. It calculates the binomial distribution probability for the number of successes from a specified number of trials. This binomial distribution Excel guide will show you how to use the function, step by step.Probability calculator is free and easy to use. You just need to follow below steps. Step #1: Define the probabilities of single or multiple events you want to calculate. Probabilities must have two separate events. Probability of A: P (A) and. Probability of B: P (B) Step #2: Find the Probability of an event.The Probability Calculator is a research tool provided to help self-directed investors model various option strategies. The criteria and inputs entered are at the sole discretion of the user and are solely for the convenience of the user. The Probability Calculator is provided by Hanweck Associates, an independent company not affiliatedRummy game free download!! poker probability calculator Download Indian rummy for free on KhelPlay Rummy.com. Visit this page to download 13 card rummy game baccarat game (free download for android). RG CREATIONS YT Illustrate Probability with Conditional Formatting. In this extension lesson, students illustrate probability data using conditional formatting in Google Sheets. Students use Google Search to find the weather forecast and then they create an event in Google Calendar.For the serial compound availability multiply the probability of each component being available: So: 99.95% * 99.95% = 0,99900025% = 99.9%. Calculating it in parallel is a little more complicated as we do need to consider what the percentage unavailability will be: The calculation is done as follows:Statistics and probability. There are 7 calculators in this category . Descriptive Statistics Calculator - Find Arithmetic mean, mode, median, minimum, maximum of a data set. Standard Deviation Calculator - Find standard deviation, variance and range of a data set. Probability Calculator - Finds conditional probability, union and intersection of events. ...Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products. Change the number of marbles of different colors in the boxes and guess the probability of drawing a red, blue, or yellow marble. Once you have decided on your answers, click the "answers" checkboxes to see if you are right.The decimal 0.167 is equal to 16.7%. To sum up, the probability of rolling a 3 with a number cube is 1 out of 6 and can be expressed in the forms explained above. In these worksheets, students will practice calculating probability. They will express probability in the form of a decimal. They will express probability in the form of a percentage.Using the Probability Template. Start by downloading this free document. All you need to do is click the link located at the bottom of this page. Below, you will notice there are 6 different tabs to use for this template. The first 4 tabs are for calculating 10, 100, 1000, 10,000. 1) Press "F9" to refresh and get different results every time.Statistics Probability cheatsheet Star 392 By Afshine Amidi and Shervine Amidi Introduction to Probability and Combinatorics Sample space The set of all possible outcomes of an experiment is known as the sample space of the experiment and is denoted by $S$. Event Any subset $E$ of the sample space is known as an event.Probability calculator is free and easy to use. You just need to follow below steps. Step #1: Define the probabilities of single or multiple events you want to calculate. Probabilities must have two separate events. Probability of A: P (A) and. Probability of B: P (B) Step #2: Find the Probability of an event.Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.First calculate Mean (average) of X Calculate Mean (average) of Y Subtract Mean of Xfrom each of Xvalues (we'll call these A), and subtract Mean of Yfrom each of Y values (we'll call these B) Square A's(we'll call these C2's) Square B's(we'll call these D2's) Multiply all A'sby B's(we'll call theseAB's) Add up all AB's Add up all C2's1.2 ml solution is diluted with 10 ml Buffer 12 µg/ml solution. (Above all so lutions are 10 µg/ml solution) Step 2: Take absorbance of all solutio n and Plot graph in MS Excel. Step 3: After ...Probability. How likely something is to happen. Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability. Tossing a Coin. When a coin is tossed, there are two possible outcomes: heads (H) or ; tails (T) We say that the probability of the coin landing H is ½The U.S. Geological Survey (USGS), in cooperation with Connecticut Department of Transportation, completed a study to improve flood-frequency estimates in Connecticut. This companion data release is a Microsoft Excel workbook for: (1) computing flood discharges for the 50- to 0.2-percent annual exceedance probabilities from peak-flow regression equations, and (2) computing additional ...ID: 994490 Language: English School subject: Math Grade/level: 5 Age: 10-12 Main content: Probability Other contents: Add to my workbooks (61) Download file pdf Embed in my website or blog Add to Google ClassroomWe can use the formula to find the chances of an event happening. Formula to Calculate Probability The formula of the probability of an event is: Probability Formula Or, P (A) = n (A)/n (S) Where, P (A) is the probability of an event “A” n (A) is the number of favourable outcomes n (S) is the total number of events in the sample space 10l_2ttl