# Solve the following problem : An examination consists of 5 multiple choice questions, in each of which the candidate has to decide which one of 4 suggested answers is correct. A completely unprepar - Mathematics and Statistics

Sum

Solve the following problem :

An examination consists of 5 multiple choice questions, in each of which the candidate has to decide which one of 4 suggested answers is correct. A completely unprepared student guesses each answer completely randomly. Find the probability that this student gets 4 or more correct answers.

#### Solution

Let X denote the number of correct questions. Since only one of 4 suggested answers is correct

P(answer is correct) = p = (1)/(4)

∴ q = 1 – p = 1 - (1)/(4) = (3)/(4)

Given, n = 5

∴ X ~ B(5, 1/4)
The p.m.f. of X is given by

P(X = x) = ""^5"C"_x (1/4)^x (3/4)^(5 - x), x = 0, 1,...,5
P(student gets 4 or more correct answers)
= P(X ≥ 4)
= P(X = 4 or X = 5)
= P(X = 4) + P(X = 5)

= ""^5"C"_4 (1/4)^4 (3/4) + ""^5"C"_5 (1/4)^5 (3/4)^(0)

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

= (15 + 1)/(4^5)

= (1)/(64).

Concept: Random Variables and Its Probability Distributions
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.08 | Page 157