Question

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	WRR	RWW	RWR	RRW	RRR
Event A: At least one red bean on the last two choices
Event B: No red beans on the first two choices
Event A and B: At least one red bean on the last two choices and no red beans on the first two choices

(b)Suppose there is at least one red bean on the last two choices. (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

B

occurs given that Event

A

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 choices

(c)Give the following probabilities and select the correct option below.

PA and BPA	=
PB|A	=
PA and BPA	▼?	PB|A

Answer 1

(a)

Event A:

P(Atleast one red bean on the last two choice) = 1 - P(no red bean on the last two choice)

= 1 - 1/4 = 3/4

Event B:

P(No red beans on the first two choices)

= 1/4

Event A and B:

The possible cases are WWR

P(at least one red bean on the last two choices and no red beans on the first two choices) = 1/8

(b)

There are 6 possibilities with event A

Possible outcomes of B conditioned on A are WWR

Thus, the required probability, P(B | A) = 1/6

(c)

P(A) = 3/4

P(B | A) = 1/6

P(B | A)*P(A) = P(A and B)