Explanation 1) Formula: Probability of the binomial experiment is given by B ( n , k ; p ) = C ( n , k ) ( p ) k ( 1 − p ) n − k Where, B ( n , k , p ) is the binomial probability, n is the number of trials in the binomial experiment, k is the number of successive trials we need in the binomial experiment, p is the probability of success in a trial. 2) Calculation: Given, A six question multiple-choice quiz, which is the trials of the experiment. In which, we need to answer at least four of the question correctly. Number of successive trials are 4,5, (or) 6 in the binomial experiment. Then, the probability of success is probability of guessing a correct answer to a question Number of outcomes = { five option with multiple choice quiz } n ( S ) = 5 Thus, probability of guessing correct answer ( p ) = 1 5 Hence, the binomial probability for 4,5 and 6 successive trials is given by, B ( 6 , 4 ; 1 5 ) , B ( 6 , 5 ; 1 5 ) and B ( 6 , 6 ; 1 5 ) Now find B ( 6 , 4 ; 1 5 ) Since, B ( n , k ; p ) = C ( n , k ) ( p ) k ( 1 − p ) n − k B ( 6 , 4 ; 1 5 ) = C ( 6 , 4 ) ( 1 5 ) 4 ( 1 − 1 5 ) 6 − 4 B ( 6 , 4 ; 1 5 ) = C ( 6 , 4 ) ( 1 5 ) 4 ( 4 5 ) 2 B ( 6 , 4 ; 1 5 ) = C ( 6 , 4 ) ( 0.2 ) 4 ( 0.8 ) 2 Find C ( 6 , 4 ) = 6 ! ( 6 − 4 ) ! 4 ! C ( 6 , 4 ) = 6 ! 2 ! 4 ! C ( 6 , 4 ) = 6 ⋅ 5 ⋅ 4 ! 2 ! 4 ! C ( 6 , 4 ) = 30 2 C ( 6 , 4 ) = 15 B ( 6 , 4 ; 1 5 ) = ( 15 ) ( 0.2 ) 4 ( 0.8 ) 2 B ( 6 , 4 ; 1 5 ) = ( 15 ) ( 0.0016 ) ( 0.64 ) B ( 6 , 4 ; 1 5 ) = 0 .01536 Next find B ( 6 , 5 ; 1 5 ) B ( 6 , 5 ; 1 5 ) = C ( 6 , 5 ) ( 1 5 ) 5 ( 1 − 1 5 ) 6 − 5 B ( 6 , 5 ; 1 5 ) = C ( 6 , 5 ) ( 1 5 ) 5 ( 4 5 ) 1 B ( 6 , 5 ; 1 5 ) = C ( 6 , 5 ) ( 0

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

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Chapter 13.5, Problem 16E

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The probability that we will answer at least four of the questions correctly by guessing.

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Chapter 13.5, Problem 15E

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The probability that we will answer at least four of the questions correctly by guessing.

Solution Summary: The author calculates the probability that we will answer at least four questions correctly by guessing. The number of successive trials is 4,5, (or) 6 in the binomial experiment.

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To find: The probability that we will answer at least four of the questions correctly by guessing.

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Chapter 13 Solutions

To find:

The probability that we will answer at least four of the questions correctly by guessing.