1. Four universities1. 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. One possible outcome can be denoted by 1324 (1 beats 2 and 3 beats 4 in iirst-round games. and then 1 beats 3 and 2 beats 4}. a. List all outcomes in .5\". b. Let A denote the event that 1 wins the tournament. List outcomes in A. :2. Let B denote the event that 2 gets into the championship game. List outcomes in 3. g d. at are the outcomes in A U B and in A n B? What are the outcomes in A'? 3. Three components are connected to iorm a system as shown in the accompanying diagram. Because the components in the 23 subsystem are connected in parallel, that subsystem will function if at least one oi the two individual components functions. For the entire system to function, component 1 must function and so must the 23 subsystem. " 9 a The experiment consists of determining the condition of each component [8 (success) for a functioning component and F (tailure) tor a noniunctioning component]. a. Which outcomes are contained in the event A that exactly two out of the three components function? to. 5 ich outcomes are contained in the event 3 that at least two of the components function? c. ich outcomes are contained in the event 0 that the system iunctions? d. List outcomes in C", A U C. A m C. B U C. and Bn 0. 8. An engineering construction firm is currently working on power plants at three different sites. Let A,- denote the event that the plant at site i is completed by the contract date. Use the operations of union, intersection, and complementation to describe each of the following events in terms of A1. A2. and A3. draw a Venn diagram, and shade the region corresponding to each one. a. At teast one plant is completed by the contract date. b. All plants are completed by the contract date. c. Only the plant at site 1 is completed by the contract date. at Exactly one plant is completed by the contract date. 9. Either the plant at site 1 or both of the other two plants are completed by the contract date