1. ÷0/8 points! Previous Answers My Notes Ask Your Teacher Natasha and Allison a

Question

1. ÷0/8 points! Previous Answers My Notes Ask Your Teacher Natasha and Allison are playing a tennis match where the winner must win 2 sets in order to win the match Natasha starts strong but tires quickly. The probability that Natasha wins the first set is 0.6. However, the probability she wins the second set is only 0.55. And if a third set is needed, the probability that Natasha wins the third set is only 0.4. Put all this information into a tree diagram to answer the following questions (a) What is the probability that Natasha wins the match? 0.475 (b) If Allison wins the first set, what is the conditional probability that Natasha, instead, ends up winning the match? 0.175 (c) If Natasha wins the first set, what is the conditional probability that Allison, instead, ends up winning the match? 0.325 (d) What is the probability that 3 sets will be played?

Explanation / Answer

Answer to the questions is as follows:

a. Natasha wins the match =

P( Natasha wins 1st and 2nd) + P(Natasha looses first and wins next 2) + P( Natasha wins 1st and 3rd)
= .6*55 + .4*.55*.4 + .6*.45*.4 = .526

b. P( natasha wins given 1st set is won by Allison)
=P( Natasha looses 1st and wins next 2 given Natasha has already lost 1st)
= 0.55*.4
= .220

c. P( Allison wins given 1st set is won by Natasha)
=P( Allison looses 1st and wins next 2 given Allison has already lost 1st)
= .6*.45
= .27

d. P( 3rd set is played) = P( this happens when both have 1 match each)
=P( Natasha wins first)*P( Allison wins 2nd) + P( Allison wins 1st) *P( Natasha wins 2nd)
= .6*.45 + .4*.55
=.49

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