Explanation Given Information: Two die red and green are rolled and X is the larger of the two numbers facing up. Formula Used: If there is a random variable X which has values x 1 , x 2 , ... , then the probability distribution of the event includes the probabilities such as X = x 1 , X = x 2 and the sum of these probabilities is always 1 . For the random variable X, P ( X = x ) represents the random variable X with the particular value of x. Calculation: Consider the probability distribution for the random variable X . Possible values of the variable X are 1 , 2 , 3 , 4 , 5 , 6 Total number of outcomes when two die rolled is 36 . The probability that number 1 appear on both dice, P ( X = 1 ) is 1 36 . The probability that either 1 or 2 appear on both die, P ( X = 2 ) = P { ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) } is 3 36 . The probability that number from 1 , 2 or 3 appear on both dice, P ( X = 3 ) = P { ( 1 , 3 ) , ( 2 , 3 ) , ( 3 , 3 ) , ( 3 , 2 ) , ( 3 , 1 ) } is 5 36 . The probability that number from 1 , 2 , 3 or 4 appear on both dice, P ( X = 4 ) = P { ( 1 , 4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , 4 ) ( 4 , 4 ) , ( 4 , 2 ) , ( 4 , 1 ) } is 7 36 . The probability that number from 1 , 2 , 3 , 4 or 5 appear on both dice, P ( X = 5 ) = P { ( 1 , 5 ) , ( 2 , 5 ) , ( 3 , 5 ) , ( 4 , 5 ) , ( 5 , 5 ) , ( 5 , 4 ) , ( 5 , 3 ) , ( 5 , 2 ) , ( 5 , 1 ) } is 9 36

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Chapter 8.1, Problem 27E

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To calculate: The value of P(X≤3), the probability distribution for the indicated random variable also sketch the histogram for the probability distribution, if two die red and green are rolled and X is the larger of the two numbers facing up.

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Chapter 8.1, Problem 26E

Chapter 8.1, Problem 28E

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The value of P ( X ≤ 3 ) , the probability distribution for the indicated random variable also sketch the histogram for the probability distribution, if two die red and green are rolled and X is the larger of the two numbers facing up.

Solution Summary: The author calculates the probability distribution for the indicated random variable X by sketching the histogram.

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To calculate: The value of P(X≤3), the probability distribution for the indicated random variable also sketch the histogram for the probability distribution, if two die red and green are rolled and X is the larger of the two numbers facing up.

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Chapter 8 Solutions