Question

A student takes an exam containing 14 true or false questions. If the student guesses, what is the probability that he will get exactly 13 questions right? Round your answer to four decimal places.

Answer 1

Let X denote number of right questions.

Total question ,n = 14

A question only has two options as answer.So probability that the question is correct is 1/2. Then p= 1/2

Also q ( failure probability) = 1-p = 1/2.

Thus, X~ B(n,p)

P( exactly 13 questions right) = P( X= 13)

=14C13 .  p​​​13​ . q

= (14) .(0.5)13 .(0.5)

= 0.000854

= 0.0009 (approx)