Mike and Jim will play tennis in \"best of 3\" sets format, but they will always

Question

Mike and Jim will play tennis in "best of 3" sets format, but they will always play the third set even though one of them has won the match by the end of the second set (unlike Problem 3 in Homework 2). Suppose that in each set, Mike and Jim may win with the same likelihood, independent with the results of previous sets. (It is like tossing a fair coin) What is the sample space Ohm in this case (use the same notations as Homework 2 Problem 3)? Is it appropriate to apply a classical probability model on this sample space? Let A denote the event that Mike wins the match, and D denote the event that Jim wins the first set. What are the probabilities of the two events A and B? Find the probability of the event C that Mike wins the first set but Jim wins the match.

Explanation / Answer

let M denote that mike win the set

while J denote that Jim win the set so

a) sample space is just like tossing of coin

sample space={(MMM),(MMJ),(MJM),(JMM),(MJJ)(JMJ)(JJM),(JJJ)}

b)

yes we can easily apply classical probability because its just like tossing a coin three times

c)

A is event that Mike wins the match while B denotes the event that Jim win the first set

since total outcomes =8

our possible outcomes i.e. A and B ={(JMM)}

so P( A and B) =1/8

c)

C={(MJJ)}

P(C) =1/8

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