Probability of independent events: Decimal answers

Question

A student ran out of time on a multiple-choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices – a, b, c, d – and only one correct answer. What is the probability that he answered both of the problems correctly?

Do not round your answer.

Answer 1

For two independent events A and B the probability of both occurring is the product of the probability of each occurring:

P(A and B) = P(A) * P(B)

Here event A - getting the first problem right - has a probability of 1/4

and event B - getting the second problem right - has the same probability of 1/4

Thus the probability of getting both right (A and B) is 1/4 * 1/4 = 1/16 = 0.0625