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, Number of question in quiz = 12 which is the trials of the experiment. In which, we need to answer at least 9 of the questions correctly. (i.e.) Number of successive trials are 9,10,11 or 12 in the binomial experiment. Then, the probability of success is probability of guessing a correct answer to a question. Number of outcomes = { C , W } n ( S ) = 2 Here, C is correct answer W is wrong answer. Thus, probability of guessing correct answer ( p ) = 1 2 Hence, the binomial probability for 9,10,11, and 12 successive trials is given by B ( 12 , 9 ; 1 2 ) , B ( 12 , 10 ; 1 2 ) , B ( 12 , 11 ; 1 2 ) and B ( 12 , 12 ; 1 2 ) Now find B ( 12 , 9 ; 1 2 ) B ( n , k ; p ) = C ( n , k ) ( p ) k ( 1 − p ) n − k B ( 12 , 9 ; 1 2 ) = C ( 12 , 9 ) ( 1 2 ) 9 ( 1 − 1 2 ) 12 − 9 B ( 12 , 9 ; 1 2 ) = C ( 12 , 9 ) ( 0.5 ) 9 ( 2 − 1 2 ) 3 B ( 12 , 9 ; 1 2 ) = C ( 12 , 9 ) ( 0.5 ) 9 ( 1 2 ) 3 B ( 12 , 9 ; 1 2 ) = C ( 12 , 9 ) ( 0.5 ) 9 ( 0.5 ) 3 B ( 12 , 9 ; 1 2 ) = C ( 12 , 9 ) ( 0.5 ) 12 B ( 12 , 9 ; 1 2 ) = C ( 12 , 9 ) ( 0 .000244140625 ) Find C ( 12 , 9 ) = 12 ! ( 12 − 9 ) ! 9 ! C ( 12 , 9 ) = 12 ! 3 ! 9 ! C ( 12 , 9 ) = 12 ⋅ 11 ⋅ 10 ⋅ ( 9 ! ) ( 3 ⋅ 2 ⋅ 1 ) ⋅ ( 9 ! ) C ( 12 , 9 ) = 1320 6 C ( 12 , 9 ) = 220 B ( 12 , 9 ; 1 2 ) = ( 220 ) ( 0 .000244140625 ) B ( 12 , 9 ; 1 2 ) ≈ 0.0537 Next find B ( 12 , 10 ; 1 2 ) B ( 12 , 10 ; 1 2 ) = C ( 12 , 10 ) ( 1 2 ) 10 ( 1 − 1 2 ) 12 − 10 B ( 12 , 10 ; 1 2 ) = C ( 12 , 10 ) ( 0.5 ) 10 ( 0.5 ) 2 B ( 12 , 10 ; 1 2 ) = C ( 12 , 10 ) ( 0

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ISBN: 9780134506470

Author: Pirnot

Publisher: PEARSON

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Chapter 13.5, Problem 15E

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The probability that we will answer at least 9 of the questions correctly by guessing.

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Chapter 13.5, Problem 14E

Chapter 13.5, Problem 16E

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The probability that we will answer at least 9 of the questions correctly by guessing.