please answer part E Mike and Jim will play tennis in \"best of 3\" sets format,
ID: 3205439 • Letter: P
Question
please answer part E
Mike and Jim will play tennis in "best of 3" sets format, meaning that one wins the match if he already wins 2 sets. They will not play the third set after the winner of the match is determined. (a) Suppose we use such letter sequence MJM to indicate the outcome that Mike wins the first and third sets and Jim wins the second set. What is the sample space Ohm (listing all elements)? Is Ohm finite, countably finite or uncountable? (b) Let A denote the event that Mike wins the match, and B denote the event that Jim wins the first set. Describe A and D by enumerating all elements in these sets. (c) Interpret the event A B, A B and A'. Describe these events by listing all elements in the sets. (d) Are A and B disjoint? (e) Express the event C = {Mike wins the first set but Jim wins the match} by using A, B and any necessary set operations.Explanation / Answer
Sample space={ MM,MJM,JMM,MJJ,JMJ,JJ}
(b) A is the event that Mike wins match
B is the event that JIM wins first set
A={ MM,MJM,JMM}
B={JMM,JMJ,JJ}
(c) AUB= event that Either A wins the match or B wins the first set
AnB=Event that A wins the match and B wins the first set
A'= Event that A doesnt wins the Match
so AUB={ MM,MJM,JMM,JMJ,JJ}
AnB={JMM}
A'={MJJ,JMJ,JJ}
(d) A and B are not Disjoint as there is a common elementary event say JMM
(e)C= {MJJ}= Compliment of (AUB)=(AUB)'= A'nB' ={MJJ,JMJ,JJ} n{MJJ,MM,MJM,JMM}={MJJ}
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