In tennis, when you serve, if the “first serve”lands in, the point is played unt

Question

In tennis, when you serve, if the “first serve”lands in, the point is played until oneof    
the players loses the point. If the first serve is out, the servercan then hit a second serve,
and that serve is played until one of the players loses thepoint. Suppose a tennis player
wins 76% of the points for which his first serve lands in (so theprobability of winning
the point if the first serve is in is .76) and 43% of the points inwhich his first serve does
not land in. Also suppose his first serve lands in for 64% ofthe points he serves. Use
this information to determine the probability that this player winsa point when he
serves.



also i am confused on this if you would like to help
Suppose that two fair dice are rolled. Consider the eventsA={sum is 7} and B={the
first die lands on 2}.
a)    Are A and B mutually exclusive? Justifyyour answer.
b)    Are A and B independent? Justify your answerwith appropriate calculations.

Explanation / Answer

1) P(player wins the points) = P(player wins point on first service) +P(player wins point on second service) first service percentage 64% second service percentage? I assume 100%, because he is a goodserver ;) Then, in 36% of the cases, the player plays a point withhis second service. From this, he wins 43% of the points. P(player wins point on first service) = 0.64*0.76 =0.4864 P(player wins point on seconde serivice) = 0.35*0.43 = 0.1548 This means that the change that the player wins the point is 0.64,which is 64% Good Luck Further For the second part: " two events are mutually exclusive if theycannot occur at the same time (i.e., they have no common outcomes).The best example is tossing a coin, which can result in eitherheads or tails, but not both. Both outcomes can't happensimultaneously." This means that the answer to question a) is no, because this canoccur at the same time. And the second part? The throws of the dices are independent. Adice is a zero'th order Markov Model/Chain. For each throw, thechange for each number is 1/6 for a fair dice. But this does not mean that the both events are independent. If thefirst dice lands on a 2, the second has to be a 5. I hope you understand this :)

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