Player V and Player M have competed against each other many times. Historical data show that cach player is cqually likely to win the first set. If Player V wins the first set, the probability that she will win the second set is 0.60. If Player V loses the first set, the probability that she wi lose the second set is 0.70. If Player V wins exactly one of the first two sets, the probability that she will win the third set is 0.45 (b) What is the probability that Player V will win a match against Player M? (c) What is the probability that a match between Player V and Player M will consist of 3 sets given that Player V wins the match? (d) What is the expected number of sets played when Player V competes in a match with Player M?

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16-12-2022
Mathematics

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Player V and Player M have competed against each other many times. Historical data show that cach player is cqually likely to win the first set. If Player V wins the first set, the probability that she will win the second set is 0.60. If Player V loses the first set, the probability that she wi lose the second set is 0.70. If Player V wins exactly one of the first two sets, the probability that she will win the third set is 0.45 (b) What is the probability that Player V will win a match against Player M? (c) What is the probability that a match between Player V and Player M will consist of 3 sets given that Player V wins the match? (d) What is the expected number of sets played when Player V competes in a match with Player M?

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-19T19:04:44+01:00

The probability of given question and values will be

a) The probability that she will win the second set is 0.60.

b) Probability that Player V will win a match against Player M is 0.35.

c) The probability that a match between Player V and Player M will consist of 3 sets given that Player V wins the match is 0.16 .

d) Probability that player V competes in a match with Player M is 0.46.

It is given in the question :

Probability that player V wins the first set : 0.5

(this is because the text says the two players are equally likely to win the first set)

- Probability that player V wins the 2nd set if he has won the 1st set : 0.6

So, the probability that player V wins the first 2 sets is: (0.5)(0.6) = 0.3

Instead, the probability that player V loses the 2nd set if he has won he 1st set is 0.40 (=1-0.60), so

So, the probabiity that player V winse the 1st set but loses the 2nd set is 0.2.

- Probability that player V loses the 1st set: 0.5

- Probability that she will lose the 2nd set in is case is 0.70, it means that the probability that she will win the 2nd set if she lost the 1st set is 0.30, So, the probability that she will lose the 1st set and win the 2nd set is:0.15.

This means that the probability that player V wins exactly 1 set out of the first two sets is: 0.2+0.15 = 0.35

At this point, the probability that she will win the 3rd set is 0.45

This means that the overall probability that she will win the 3rd set if she won exactly 1 of the first 2 sets is: (0.35)(0.45) = 0.16

So, the overall probability that player V will win a match against player M is : 0.30+0.16 = 0.46.

To know more about probability, go to:

brainly.com/question/30034780

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