A multiple choice test consists of 5 questions, each with 4 possible answers. An instructor will pass any student who can answer at least 1 question correctly. What is the probability that a student will pass using random guessing alone? 1. 0.7627 2. 0.2373 3. 0.8571 4. 0.25

gemauert79 2022-09-17 Answered
A multiple choice test consists of 5 questions, each with 4 possible answers. An instructor will pass any student who can answer at least 1 question correctly. What is the probability that a student will pass using random guessing alone?
1. 0.7627
2. 0.2373
3. 0.8571
4. 0.25
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Answers (1)

hampiova76
Answered 2022-09-18 Author has 5 answers
Let x be number of questions correct. Here x follows binomial distribution with parameters n = 5 and p = 1 4 = 0.25
The pdf of binomial distribution is,
P ( X = x ) = ( n x ) p x ( 1 p ) n x ; x = 0 , 1 , 2...
The probability that a student will pass using random guessing alone is,
P ( X 1 ) = P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) = ( 5 1 ) ( 0.25 ) 1 ( 1 0.25 ) 5 1 + ( 5 2 ) ( 0.25 ) 2 ( 1 0.25 ) 5 2 + ( 5 3 ) ( 0.25 ) 3 ( 1 0.25 ) 5 3 + ( 5 4 ) ( 0.25 ) 4 ( 1 0.25 ) 5 4 + ( 5 5 ) ( 0.25 ) 5 ( 1 0.25 ) 5 5 = 0.3955 + 0.2637 + 0.0879 + 0.0147 + 0.0010 = 0.7627

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