Tony rolls a fair number cube numbered 1 to 6 and tosses a fair coin. Which expression could be used to determine the probability that he rolls an even number and tosses a “tails”?

Question

A. 1/6 * 1/2

B. 1/3 * 1/2

C. 1/2 + 1/2

D. 1/2 * 1/2

Answer 1

First the two events are independent so if we let P(A) = Prob(rolling an even number) and P(B) = Prob(of tossing a tail), then there are 3 possible even numbers on a fair die of 6 sides, so this probability = 3/6 or 1/2, Likewise, there is one way to roll a tail with two sides, so this probability is 1/2, and thus because of independence, the total Probability of the two events is P(A)* P(B) = 1/2 * 1/2, Answer D