Hi! I need help with these questions.

Problem 13 Two teams A and B play a soccer match, and we are interested in the winner. The sample space can be defined as S = {a, b, d }, where a shows the outcome that A wins, b shows the outcome that B wins, and a shows the outcome that they draw. Suppose we know that: (1) the probability that A wins is P(a) = P(la}) = 0.5; (2) the probability of a draw is P(d) = P((d) ) = 0.25. a. Find the probability that B wins. b. Find the probability that B wins or a draw occurs.Problem 17 Four teams A, B, C, and D compete in a tournament, and exactly one of them will win the tournament. Teams A and B have the same chance of winning the tournament. Team C is twice as likely to win the tournament as team D. The probability that either team A or team C wins the tournament is 0.6. Find the probabilities of each team winning the tournament. Problem 22 Suppose that, of all the customers at a coffee shop, 0 70% purchase a cup of coffee; 0 40% purchase a piece of cake; 0 20% purchase both a cup of coffee and a piece of cake. Given that a randomly chosen customer has purchased a piece of cake, What is the probability that he/ she has also purchased a cup of coffee? Problem 23 Let A, B, and C be three events with probabilities given below: 21. Find P(A|B). b. Find P(C|B). c. Find P(B|A u C). d. Find P(B|A, C) = P(B|A n C). Problem 25 A professor thinks students who live on campus are more likely to get AS in the probability course. To check this theory, the professor combines the data from the past few years: a. 600 students have taken the course, b. 120 students have gotten As, c. 200 students lived on campus, d. 80 students lived off campus and got AS. Does this data suggest that "getting an A" and "living on campus" are dependent or independent