Explanation Given Information: Two die are weighted such that the number out of 2 , 3 , 4 , 5 is half as likely to face up as each of 1 and 6 where X is the number of 1 s that face up when both are thrown. Formula Used: If n is the number of trials and X is the number of successes, then the probability for particular value of X is given by: P ( X = x ) = C ( n , x ) p x q n − x Where C ( n , r ) = n ! r ! ( n − r ) ! . Calculation: Consider the random variable X, two die are rolled. Total number of outcomes for single die, n = 6 . Assume, the probability of the numbers 2 , 3 , 4 , 5 facing up be p and probability of facing 1 and 6 be 2 p . Possible number of outcomes of random variable X, when a die is rolled is 1 , 2 , 3 , 4 , 5 , 6 . x 1 2 3 4 5 6 P ( X = x ) 2 p p p p p 2 p Since the sum of all probabilities is always 1 . Evaluate the probability p. 2 p + p + p + p + p + 2 p = 1 8 p = 1 p = 1 8 Thus, the probability distribution when a single die is rolled, x 1 2 3 4 5 6 P ( X = x ) 1 4 1 8 1 8 1 8 1 8 1 4 Therefore, the probability of success that 1 s face up when both are thrown p = 1 4 . Evaluate the probability of failure, q . q = 1 − 1 4 = 3 4 Possible number of outcomes when two die are rolled that 1 s face up are 0 , 1 , 2 . Evaluate the probability, P ( X = 0 ) by use of the formula P ( X = x ) = C ( n , x ) p x q n − x P ( X = 0 ) = C ( 2 , 0 ) ( 1 4 ) 0 ( 3 4 ) 2 − 0 = 2 ! 0 ! ( 2 − 0 ) ! × 1 × ( 3 4 ) 2 = 1 × 1 × 0

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Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 8, Problem 6RE

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To calculate: The probability distribution of random variable X if 2 die are weighted such that the number out of 2,3,4,5 is half as likely to face up as each of 1 and 6 where X is the number of 1s that face up when both are thrown.

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Chapter 8, Problem 5RE

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Chapter 8 Solutions

Finite Mathematics

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The probability distribution of random variable X if 2 die are weighted such that the number out of 2 , 3 , 4 , 5 is half as likely to face up as each of 1 and 6 where X is the number of 1 s that face up when both are thrown.

Solution Summary: The author calculates the probability distribution for the number of 1s that face up when both are thrown.

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To calculate: The probability distribution of random variable X if 2 die are weighted such that the number out of 2,3,4,5 is half as likely to face up as each of 1 and 6 where X is the number of 1s that face up when both are thrown.

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