An experiment consists of first rolling a die and then tossing a coin. (a) List the sample space. {(1, H), (2, H), (3, H), (4, H), (5, H), (6, H)} {(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)} {(3, H), (4, H)} {(1, T), (2, T), (3, T), (4, T), (5, T), (6, T)} {(3, H), (3, T), (4, H), (4, T)}
(b) Let A be the event that either a three or a four is rolled first, followed by landing a head on the coin toss. Find P(A). (Enter your probability as a fraction.)
P(A) =
(c) Suppose that a new experiment consists of first rolling a die and then tossing a coin twice. Let B be the event that the first and second coin tosses land on heads. Let C be the event that either a three or a four is rolled first, followed by landing a head on the first coin toss. Are the events B and C mutually exclusive? Explain your answer.
A. Events B and C are mutually exclusive because they have different probabilities.
B. Events B and C are mutually exclusive because the first and second coin tosses cannot land on heads when a three or four is rolled first.
C. Events B and C are not mutually exclusive because the first and second coin tosses can land on heads when a three or four is rolled first.
D. Events B and C are mutually exclusive because they are dependent events.