A test consists of ten true/false questions. A student who forgot to study guesses randomly. What is the probability that the student answers exactly five questions correctly?

Answer 1

The binomial probability formula can be applied to this problem.

Probability of x successes in n tries, where each try has identical probability of success p:

C p^x (1-p)^(n-x)

n x

For this problem n = 10, x = 5 and p = 0.5 (since 50% change guess the correct answer)

C 0.5^5 (1-05)^(10-5)

10 5

252 * 0.5^10 = 0.246