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.

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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.

(a) Check the outcomes for each of the three events below. Then, enter the probability of each event.
Outcomes
Probability
WWW WWR WRW WRRRWW RWR RRW RRR
Event A: The first bean is white
Event B: At least two beans are white
Event A and B: The first bean is white
and at least two beans are white
Transcribed Image Text:(a) Check the outcomes for each of the three events below. Then, enter the probability of each event. Outcomes Probability WWW WWR WRW WRRRWW RWR RRW RRR Event A: The first bean is white Event B: At least two beans are white Event A and B: The first bean is white and at least two beans are white
(b) Suppose the first bean is white. (That is, Event A occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event
B. Then, enter the probability that Event
Occurs given that Event A occurs.
Outcomes glven the first bean is white
Probability
www.wwR|WRW WRR
Event B: At least two beans are white
(c) Give the following probabilities and select the correct option below.
P(4 and B)
P()
P(BLA)
P(A and B)
P(A)
P(B|4)
Transcribed Image Text:(b) Suppose the first bean is white. (That is, Event A occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event B. Then, enter the probability that Event Occurs given that Event A occurs. Outcomes glven the first bean is white Probability www.wwR|WRW WRR Event B: At least two beans are white (c) Give the following probabilities and select the correct option below. P(4 and B) P() P(BLA) P(A and B) P(A) P(B|4)
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