Exercise 1.41. Imagine a game of three players where exactly one player wins in the end...

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Exercise 1.41. Imagine a game of three players where exactly one player wins in the end and all players have equal chances of being the winner. The game is repeated four times. Find the probability that there is at least one person who wins no games. Hint. Let A = {person i wins no games} and utilize the inclusion-exclusion for- mula. Exercise 1.42. Suppose P(A) > 0.8 and P(B) > 0.5. Show that P(AB) > 0.3. Exercise 1.41. Imagine a game of three players where exactly one player wins in the end and all players have equal chances of being the winner. The game is repeated four times. Find the probability that there is at least one person who wins no games. Hint. Let A = {person i wins no games} and utilize the inclusion-exclusion for- mula. Exercise 1.42. Suppose P(A) > 0.8 and P(B) > 0.5. Show that P(AB) > 0.3.