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 first 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. (If necessary, consult a list of formulas.) (a) Check the outcomes for each of the three events below. Then, enter the probability of each event. Outcomes Probability WWW WWR WRW WRR RWW RWR RRW RRR Event A: At least one red bean on the I] last two choices Event B: No red beans on the first two I] choices Event A and B: At least one red bean on the last two choices and no red beans on I] the first two choices (b) Suppose there is at least one red bean on the last two choices. (That is, EventA occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event B. Then, enter the probability that Event B occurs given that Event A occurs. (b) Suppose there is at least one red bean on the last two choices. (That is, EventA occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event B. Then, enter the probability that Event B occurs given that EventA occurs. Outcomes given there is at least one red bean on the last tWO choices Probability WWR WRW WRR RWR RRW RRR Event B: No red beans on the first two I] choices (c) Give the following probabilities and select the correct option below. P(A and B) P(A) = '1 P(B|A) = I] P (A and B) P(A) ? VP(B|A)