A biology professor gives a surprise quiz consist of a true/false question followed by a multiple choice question with four possible answers. If both questions are answered with random guesses, find the probability that both responses are correct. Please show your work.

What is (1/4)(1/4) ?

To solve this problem, we need to find the probability of getting both questions correct given that the answers are random guesses.

For the true/false question, we have a 1/2 chance of guessing correctly since there are only two options.

For the multiple-choice question, we have a 1/4 chance of guessing correctly since there are four options.

To find the probability of getting both questions correct, we multiply the probabilities of each question being answered correctly:

P(both correct) = P(true/false correct) * P(multiple-choice correct)
= 1/2 * 1/4
= 1/8

Therefore, the probability that both responses are correct is 1/8 or 0.125.