Find the probability that $$X$$ is even. Find the distribution of $$X$$. 3.20 This riddle is a common interview problem: A king has imprisoned 10 subjects. He offers the prisoners a strange way that they can play for their release: each day, he will randomly and independently call one of the 10 prisoners in.
new probability for an event Fthe conditional probability of Fgiven Eand denote it by P(FjE). Example 4.1 An experiment consists of rolling a die once. Let Xbe the outcome. Let F be the event fX =6g, and let E be the event fX>4g. We assign the distribution function m(!)=1=6 for! =1;2;:::;6. Thus, P(F)=1=6. Now
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Exercise 4.1. Find the pmf and the CDF of the number of heads obtained in four tosses of a fair coin and plot the CDF. Exercise 4.2. Suppose a fair die is rolled twice and that X is the absolute value of the difference of the two rolls. Find the pmf...

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• A fair, six-sided die is rolled. Describe the sample space S , identify each of the following events with a subset of S and compute its probability (an outcome is the number of dots that show up). a.
• Probability that 2 or more independent events will happen is the PRODÜCT of their separate probabi I i ties. (1/2) (1/2) = tossing 2 coins and having both turn-up heads — 1/4 tossing 2 dice and getting a sum of 6: here we must find all possible outcomes that satisfy each event (sum) 2nd- 1 die 1st die P (s of 6) ways to roll a 6 36 10 [ SUMS] 10

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Find the probability that the first runner across the finish line is from Team $$A$$. Rolling Dice; Suppose you roll three fair dice. How many possible outcomes are there? Find the probability you roll three sixes. Find the probability that all three dice show the same number. Find the probability that the sum of the dice is equal to 10.

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For example, the probability of rolling a one with a six-sided die is 1/6. When rolling two dice with six sides each there are 1/6 X 1/6 = 1/36 probability of rolling double ones. You can verify this probability on the table below. Notice there is only one cell with double ones and there are 36 (6 × 6) cells in total.

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The basic idea of theoretical probability when all outcomes are equally likely is the total number of ways an event can happen divided by the total possible outcomes. For example, the theoretical probability of rolling a two or four on six-sided die is 2/6 or 1/3 since there are two ways to get a two or four out of six possible outcomes.

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The probability of rolling a number less than 5 is Check Point2 A die is rolled. Find the probability of getting a number greater than 4. Computing Theoretical Probability Two ordinary six-sided dice are rolled.What is the probability of getting a sum of 8? Solution Each die has six equally likely outcomes. By the Fundamental

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