Question

A multiple-choice test consists of 6 questions. Each question has answer choices of a , b , c , and d , and only one of the choices is correct. If a student randomly guesses on each question, what is the probability that she gets fewer than 3 of them correct?

Answer 1

Given that there are n = 6 questions.

each question has 4 choices. i.e p = 1/4

We have to find the P(X<3)

that is we have to find

Where X has binomial distribution with n = 6 and p = 1/4 = 0.25

So ,

Where x! = x(x-1) (x-2) ....2*1

example 3! = 3*2*1 = 6

P(X = 0) = 0.1780

Simmilarly we will get,

P(X = 1) = 0.3560

and P(X = 2) = 0.2966

so, P(X <= 2) = P(x= 0)+P(x = 1) +P(x =2 ) = 0.1780 +0.3560 +0.2966

P(X < = 2) = 0.8306

Answer: 0.8306