Four universities—1, 2, 3, and 4—are participating in a holiday basketball tournament. In the first round, 1 will play 2 and 3 will play 4. Then the two winners will play for the championship, and the two losers will also play. One possible outcome can be denoted by 1324 (1 beats 2 and 3 beats 4 in first-round games, and then 1 beats 3 and 2 beats 4). a. List all outcomes in . b. Let A denote the event that 1 wins the tournament. List outcomes in A. c. Let B denote the event that 2 gets into the championship game. List outcomes in B. d. What are the outcomes inA ?B and in A?B? What are the outcomes in A?

Solution: Step 1: It is given that, four universities 1, 2, 3, and 4are participating in a holiday basketball tournament. In the first round, 1 will play 2 and 3 will play 4. Then the two winners will play for the championship, and the two losers will also play. Step 2: a) we need the list of all possible outcomes Since it is given that in the first round 1(university)will play with 2 and 3 will play with 4 and also the winners will play for the championship and losers will also play so there will be eight possible outcomes. (If 1324 means 1 beats two and 3 beats 4 in the first round, then 1 beats 3 and 2 beats4) 1)1324 5) 3142 2)2413 6)3241 3) 1423 7)4132 4) 2314 8)4231 b) If A denote the event that 1 wins the tournament the outcome of the event will be in the form( means 1 can beat 3 or 4 in the final round). 1) 1324 2) 1423 step3: c) It is given that the event B denote that 2 gets into the championship we know that 1 always play with 2 in the starting. so the possible outcome will be in the form. 1) 2314 2) 4231 3) 3241 4) 2413