Probability of Outcomes Practice Test

A fair coin is flipped repeatedly until either 3 consecutive heads or 3 consecutive tails appear. What is the probability that the sequence ends with 3 consecutive heads?

Two events A and B are such that P(A) = 0.6, P(B) = 0.4, and P(A ∪ B) = 0.8. If event C is independent of both A and B, and P(C) = 0.3, what is P((A ∩ B) ∪ C)?