Please answer these questions with explanation

2. A baseball player compiles the following information: He hits a homerun (H) in 34% of his games. He gets a strikeout (S) in 40% of his games. _ In 78% of his games, he hits a home run (H) or his team wins (W). In 10% of his games, he hits a home run (H)and gets a strikeout (S) _ In 26% of his games, he hits a home run (H) and his team wins (W). _ In 28% of his games, he gets a strikeout and his team wins. (a) In any given game, what is P(H or S)? (b) What is P(W)? (c) What is P(H and W5)? 3. There were 13 games scheduled one Sunday in the National Football League. The games and probabilities of each team winning their respective games are shown below: Game 1: Houston (0.55) vs. Buffalo (0.45) Game 2: Cleveland (0.20) vs. Chicago (0.80) Game 3: Seattle (0.17) vs. Dallas (0.83) Game 4: St. Louis (0.21) vs. Detroit (0.79) Game 5: Denver (0.13) vs. Baltimore (0.87) Game 6: San Francisco (0.88) vs. Indianapolis (0.12) Game 7: Miami (0.18) vs. Jets (0.82) Game 8: Tampa Bay (0.42) vs. Giants (0.58) Game 9: Jacksonville (0.44) vs. Tennessee (0.56) Game 10: Oakland (0.27) vs. San Diego (0.73) Game 11: Carolina (0.36) vs. Arizona (0.64) Game 12: Minnesota (0.08) vs. Green Bay (0.92) Game 13: Atlanta (0.42) vs. New Orleans (0.58) (a) The outcome of interest is the winners of each of the first 5 games. How many outcomes are contained in the appropriate sample space? (b) What is the probability that Denver or the Giants win? Solution: (c) Looking at game 7, 8 and 9 only. What is the probability that exactly two of the three teams from Florida win their games? (Florida teams are shown in bold.) 4. Suppose the probability that a hockey team wins any given game is 60% and that the outcomes of the games are independent. Also assume that none of these games will end in a tie. (a) The outcome of interest is whether the team wins or loses each of its first three games. List the complete sample space of outcomes and calculate the probability of each of the outcomes. (b) Let X be the number of its first three games that the team wins. Find the probability distribution of X