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