# On a Multiple Choice Examination with Three Possible Answers for Each of the Five Questions, What is the Probability that a Candidate Would Get Four Or More Correct Answers Just by Guessing? - Mathematics and Statistics

Sum

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

#### Solution

The repeated guessing of correct answers from multiple-choice questions is Bernoulli trials. Let X represent the number of correct answers by guessing in the set of 5 multiple-choice questions.

Probability of getting a correct answer is, p = 1/3

 therefore q = 1 - p = 1 -1/3 = 2/3

Clearly, X has a binomial distribution with n = 5 and p = 1/3.

The p.m.f. of X is given by

P(X = x) = "^nC_x  p^x  q^(n - x), x = 0, 1, 2, 4, 5

i.e. p(x) = "^nC_x (1/3)^x (2/3)^(5-x) x = 0, 1, 2, 3, 4, 5

P(four or more correct answers) = P[X ≥ 4] = p(4) + p(5)

= ""^5C_4 (1/3)^4 (2/3)^(5 - 4) + "^5C_5 (1/3)^5 (2/3)^(5 - 5)

= 5xx(1/3)^4 xx (2/3)^1 + 1xx (1/3)^5 (2/3)^0

= (1/3)^4  [5 xx 2/3 + 1/3]

= (1/3)^4 [10/3 +1/3] = 1/81 xx 11/3 = 11/243

Hence, the probability of getting four or more correct answers 11/243.

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#### APPEARS IN

NCERT Class 12 Maths
Chapter 13 Probability
Q 9 | Page 577