Explanation Given information: The binomial experiment with probability of success p = 0.2 is performed 7 times. Concept used: Binomial experiment is a experiment that results in two outcomes, success and failure. The probability of success is represented by p and probability of failure is represented by 1 − p . The probability of getting exactly r successes in n independent trials of the experiment can be calculated as, P ( r successes ) = C ( n , r ) p r ( 1 − p ) n − r ...... (1) Here, n and r are positive integers. Calculation: It is given that the number of independent trials is 7, therefore the value of n is 7. Now, substitute 7 for n, 0.2 for p and 0 for r in equation (1) to obtain the probability of for no success. P ( r = 0 ) = C ( 7 , 0 ) ( 0.2 ) 0 ( 1 − 0.2 ) 7 − 0 = 7 ! 0 ! ( 7 − 0 ) ! ( 1 ) ( 0.8 ) 7 = 1 ( 1 ) ( 0.2097152 ) = 0.2097152 Substitute 7 for n, 0.2 for p and 1 for r in equation (1) to obtain the probability of for one success. P ( r = 1 ) = C ( 7 , 1 ) ( 0.2 ) 1 ( 1 − 0.2 ) 7 − 1 = 7 ! 1 ! ( 7 − 1 ) ! ( 0.2 ) 1 ( 0.8 ) 6 = 7 ( 0.2 ) ( 0.262144 ) = 0.3670016 Substitute 7 for n, 0.2 for p and 2 for r in equation (1) to obtain the probability of for two successes. P ( r = 2 ) = C ( 7 , 2 ) ( 0.2 ) 2 ( 1 − 0.2 ) 7 − 2 = 7 ! 2 ! ( 7 − 2 ) ! ( 0.2 ) 2 ( 0.8 ) 5 = 21 ( 0.04 ) ( 0. ) = 0.2752512 Substitute 7 for n, 0.2 for p and 3 for r in equation (1) to obtain the probability of for three successes. P ( r = 3 ) = C ( 7 , 3 ) ( 0.2 ) 3 ( 1 − 0.2 ) 7 − 3 = 7 ! 3 ! ( 7 − 3 ) ! ( 0.2 ) 3 ( 0.8 ) 4 = 35 ( 0 To determine (b) To sketch: The probability histogram for different outcomes in a binomial experiment.

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 9.3, Problem 19E

To determine

(a)

To sketch:

The table of probability distribution for the binomial experiment.

To determine

(b)

To sketch:

The probability histogram for different outcomes in a binomial experiment.

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Chapter 9.3, Problem 18E

Chapter 9.3, Problem 20E

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(a) To sketch: The table of probability distribution for the binomial experiment.

Solution Summary: The author illustrates the probability distribution for the binomial experiment, which results in two outcomes, success and failure.