Question

Suppose you are taking an exam that only includes multiple choice questions. Each question has four possible choices and only one of them is correct answer per question. Questions are not related to the material you know, so you guess the answer randomly in the order of questions written and independently. The probability that you will answer at most one correct answer among five questions is ?

Answer 1

Here, n = 5, p = 0.25, (1 - p) = 0.75 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 1).
P(X <= 1) = (5C0 * 0.25^0 * 0.75^5) + (5C1 * 0.25^1 * 0.75^4)
P(X <= 1) = 0.2373 + 0.3955
P(X <= 1) = 0.6328

Ans: 0.6328