Question

A researcher asks 4 students the same “Yes/No” question. If students are independent and there is a 70% chance of a student answering “NO”, find the probability exactly 2 answer “NO”.

(A) 0.348

(B) 0.735

(C) 0.132

(D) 0.265

Answer 1

Solution

Given that ,

p = 0.70

1 - p =0.30

n = 4

x = 2

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X = 2) = ((4! / 2! (4-2)!) * 0.70 ²* (0.30)^4-2

=  ((4! / 2! (2)!) * 0.70² * (0.30)²

= 0.2646

Probability = 0.265

Option D) is correct.