do part b c

The following examples help to illustrate these concepts. When a batter is , two events of interest are "the batter reaches base safely" (Event A [O,02,06]) and "the batter hits the ball(Event B [0,,04,03,0,1), using the definitions from Example 3.1. 1. The complements of these events are, respectively, the batter does not reach base safely" (A) and "the batter does not hit the ball (B) = [03, 04, 05] B = (O2,03] 2. The intersection of A and B is the event "batter reaches base safely as the result of hitting the ball," and so, ANB= [01,06] (3.1) 3. The union is the event "the batter reaches base safely or the batter hits the ball," and so, AU B = [01, 02, 04, 05, 06] (3.2) 4. Note that the events A[O1, O2,06] and [03, 04, 05] are mutually exclusive since their intersection is the empty set and collectively exhaustive since their union is the sample space S, that is, AU = [0,, 02, 03, 04, 05, 06] The same statements apply for B[01, 04, 05, 06 ] and B [O2, O3). Consider also the intersection of events A[O3, 04, 05] and B[01, 04, 05, 06). The events Oy, "ground ball out," and Oz, fly ball out," represent the condition where the batter hits the ball but makes an out. ICCI sec. We designate four basic outcomes for the Dow Jones Industrial average over two con- secutive days: 0,: The Dow Jones average rises on both days. 02: The Dow Jones average rises on the first day but does not rise on the second day. Oz: The Dow Jones average does not rise on the first day but rises on the second day. 04: The Dow Jones average does not rise on either day. Clearly, one of these outcomes must occur, but more than one cannot occur at the same time. We can, therefore, write the sample space as S [O1, O2, O3, 04]. Now, we consider these two events: A: The Dow Jones average rises on the first day." B: "The Dow Jones average rises on the second day." Find the intersection, union, and complement of A and B. =