Statistics problem about tossing a coin

Question

An experiment consists of first rolling a die and then tossing a coin.
a. List the sample space.
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).
c. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive?
Explain your answer in one to three complete sentences, including numerical justification.

Answer 1

sample space has 12 events

1, 2, 3, 4, 5, 6 each with H

and six more each with T

P(3 or 4 with H) = 2/12 = 1/6

P(B) involves 2 coin tosses. A just has 1 coin toss. Event B has Event A as a subset