Question

a test is conducted which is consisting of 20 mcqs (multiple choices questions) with every mcq having its four options out of which only one is correct. determine the probability that a person undertaking that test has answered exactly 5 questions wrong. hint p=1/4.

Answer 1

1. If he answered 5 wrong questions then he would have been answered 15 questions perfectly
2. Hence probability of answering 15 correct questions out of 20 is =15/20 which is also equal to answering exactly 5 wrong answers

Answer 2

Concept-

Use the concept of binomial distribution to find the probability of giving exactly 5 questions wrong.

Given-

There are total 20 multiple choice questions with every MCQ having 4 options and out of 4 options only 1 option is correct.

Find-

Find the probability that a person giving the test has answered exactly 5 questions wrong.

Solution-

It is given that n = 20

P(correct) = 1/4 = 0.25

P(wrong) = 3/4 = 0.75

Hence, it follows binomial distribution

P(X = x) = xⁿ. (P)ˣ. (1-P)ⁿ⁻ˣ

⇒ P (Exactly 5 questions wrong )

⇒ P(X = 5) = (5)^20 . (0.75)^5 . (0.25)^20-5

⇒ 15504 . (0.237304688) . (0.000000000931322575)

⇒ 0.00000342649583

⇒ 0.00000343

Therefore, the probability of exactly 5 questions wrong are 0.00000343.

#SPJ2