Question

A student takes an exam containing 11 11 true or false questions. If the student guesses, what is the probability that he will get exactly 3 3 questions right? Round your answer to four decimal places.

Answer 1

Solution

Given that ,

p = 1 / 2 = 0.5

1 - p = 1 - 0.5 = 0.5

n = 11

x = 3

Using binomial probability formula ,

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

P(X = 3) = ((11! / 3! (11 - 3)!) * 0.5³ * (0.5)^{11 - 3}

=  ((11! / 3! (8)!) * 0.5³ * (0.5)⁸

= 0.0806

Probability = 0.0806