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The probability that George beats Larry in a tennis match is 0.75. If they play 2 tennis matches, what is the probability that George wins the first or second match but not both?

I have no idea where to begin!

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Required Probability = p(Loses first, Wins Second) + p(Wins first, Loses second) Probability of Winning = 0.75 Probability of Losing =

1-0.75 = 0.25


Answer = 0.25*0.75 + 0.75*0.25

(This assumes independence and mutual exclusivity. The former is assumed when we compute p(Loses first, Wins second) as a direct product of the 2 events' probabilities and the latter when we add the two terms together.)

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Hint: You have two possibilities: George wins the first and Larry wins the second, or Larry wins the first and George wins the second. You have to assume the two matches are independent, and the two possibilities cannot both happen. Does that help?

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The first match and the second match are independent; that is, if someone wins or loses the first match, that doesn't change the probability that they win or lose the second match, and vice versa.

Given two independent events $A$ and $B$, $$P(A\text{ and }B)=P(A)\times P(B).$$ Use this formula to find the probability that both event $A$ and event $B$ occur, where event $A$ is that George wins the first match and event $B$ is that George loses the second. Then use it again to find the probability he loses the first match and wins the second.

Since these two options are mutually exclusive (they can't both happen), the probability that one or the other happens is the sum of the probabilities of each of them.

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