An unbiased die is tossed twice. What is the probability of getting a 4,5 or 6 on the first toss and a 1,2,3 or 4 on the second toss?

Step-by-step solution

The sample space for tossing an unbiased die twice consists of 6 6 = 36 equally likely outcomes. Let A be the event of getting a 4, 5, or 6 on the first toss. The number of favorable outcomes for the first toss is 3, so P(A) = 3 6 = 1 2 . Let B be the event of getting a 1, 2, 3, or 4 on the second toss. The number of favorable outcomes for the second toss is 4, so P(B) = 4 6 = 2 3 . Since the two tosses are independent events, the probability of both events occurring is P(A B) = P(A) P(B) . P(A B) = 1 2 2 3 = 1 3 .