4%points Four universities-1, 2, 3, and 4-are participating EMPTY or % for the e

Question

4%points Four universities-1, 2, 3, and 4-are participating EMPTY or % for the empty set.) 2.1 in a holiday basketball tournament. In the first round, 1 will play 2 and 3 will play 4. Then the two winners will play fer the championship, and the Enter basketball tournament. In two losers will also play. One possible outcome can be denoted by 1324 (1 beets 2 and 3 beats 4 in first-round games, and then 1 beats 3 and 2 beats 4). (Enter your answers in set notation. (a) List all outcomes in S 1324,2413,2314,1423x (b) Let A denote the event that 1 wins the tournament. List outcomes in A. A-1 (1324,1342,1423,1432) |- (c) Let B denote the event that 2 gets into the championship game. List outcomes in B 2314,2341,3214,3241,2413,2431,4213,4231 (d) What are the outcomes in AUB? AUB1324,1342,1423,1432,2314,2341,3214,3241,2413,2431,4213,4231 What are the outcomes in A n B An8 EMPTY What are the outcomes in A' A- 2413,2431,4213,4231,2314,2341,3241,3214,2413,2431,4213,2431) x

Explanation / Answer

(a) The number of possible number for first two places is 4, they are 13,14,23,24 and the next two places can be taken by 4 values 24,23,14,13 respectively but in a different order. So, the total number of outcomes = 4*4 = 16.

All outcomes in S is {2413,2431,4213,4231,1423,1432,4123,4132,1324,1342,3142,3124,2314,2341,3214,3241}.

(f) We need to calculate the outcomes in A'

from question (b) we came to know that A={1324,1342,1423,1432}

So, A' = S - A= {2413,2431,4213,4231,4123,4132,3142,3124,2314,2341,3214,3241}

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