stats and prob

V Three beans are selected from a large jar containing equal amounts of white beans and red beans. An outcome is represented by a string of the sort RWW (meaning the rst bean is red, the second is white, and the third is white}. The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions. (a) Check the outcomes for each of the three events below. Then, enter the probability of each event. Outcomes WWW WWR WRW WRR RWW RWR RRW RRR Probability Event A: Alternating white and red (with C1 C1 C1 C1 C1 C1 C1 C1 either coming rst) Event 3: Exactly one bean is red 0 r1 m m m r1 m m Event A and B: Alternating white and red (with either coming rst) and exactly one F1 F1 F1 F1 F1 F1 F1 F1 bean is red (b) Suppose exactly one bean is red. (That is, Event B occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event A. Then, enter the probability that EventA occurs given that Event 3 occurs. Outcomes given exactly one bean is red WWR WR W R WW Probability Event A: Alternating white and red (with m m 0 either coming rst) (c) Give the following probabilities and select the correct option below. P (A and B) P(B) X 5 ? P(AB) = P(A and B) P(B) ? P(AB)