Question

There are two jars, A and B. Jar A contains 7 red and 2 blue marbles, while jar B contains 5 red and 4 blue marbles. You roll a fair die.If you get a 2 or a 3, you pick a random marble from jar A and put it in jar B. You then pick a random marble from jar B.
Else you pick a random marble from jar B and put it in jar A. You then pick a random marble from jar A.
a.What is the probability that you end up with a blue marble?
b.What is the probability that you moved a blue marble, given you ended with a blue marble?
c.What is the probability that you rolled a 2 or 3, given that you ended with a blue marble?
d.What is the probability that you end with a blue marble, given that you moved a red marble?

Answer 1

a. 7/2