Question

A "True or False" test has five questions.

If you guess the answers, what is the
probability that you will get exactly two
correct?​

Answer 1

5/16.

Explanation:

The probability of getting a correct answer on one question is 1/2 and the probability of getting it wrong is 1 - 1/2 = 1/2.

The probability of the first 2 being correct and the next 3 wrong = (1/2)^5 = 1/32.

There are 10 possible combinations of this ( first wrong the 2nd and third right and last 2 wrong, etc).

So the required probability is 10 * 1 /32

= 10/32

= 5/16.