Question

A test contains 10 multiple-choice questions. Each question has 4 answers and only 1 answer is correct. Suppose a student just randomly selects an answer for each question. What is the probability that the student will answer 2 or fewer questions correctly?

Answer 1

Solution

Given that ,

p = 1 / 4 = 0.25

1 - p = 1 - 0.25 = 0.75

n = 10

Using binomial probability formula ,

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

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

=  ((10! / 0! (10)!) * 0.25⁰ * (0.75)¹⁰ +  ((10! / 1! (9)!) * 0.25¹ * (0.75)⁹ +   ((10! / 2! (8)!) * 0.25² * (0.75)⁸

= 0.0547

Probability = 0.0547