Mike and Jim will play tennis in \"best of 3\" sets format, meaning that one win
ID: 3203952 • Letter: M
Question
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 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 2 (listing all elements)? Is 2 finite, countable finite or uncountable? Let A denote the event that Mike wins the match, and B denote the event that Jim wins the first set. Describe A and B by enumerating all elements in these sets. Interpret the event A B, And and A'. Describe these events by listing all elements in the sets Are A and B disjoint? Express the event C {Mike wins the first set but Jim wins the match) by using A, and any necessary set operations.Explanation / Answer
a) Suppose we use such letter sequence MJM to indicate the outcome that Mike wins the first and third sets and Jim wins second set.
Sample space is
= { MM, JJ, MJM, MJJ, JMJ, JMM } = 6
The outcomes are finite.
b)
A = { MM, MJM, JMM }
B = { JJ, JMJ, JMM }
c)
Union mean all element of both events but not same repeated.
A B = { MM, JJ, MJM , JMJ, JMM }
Intersection means comman elements.
A B = { JMM }
Complement means elements which are not in event A
and A = { JJ, JMJ, MJJ }
d) The sets A and B are not disjoint becuase they have a common element 'JMM'.
e)
C = {Mike wins the first set but Jim wins the match}
= A' B'