Question

Urn A contains 5 green and 4 red balls, and Urn B contains 3 green and 6 red balls. One ball is drawn from Urn A and transferred to Urn B. Then one ball is drawn from Urn B and transferred to Urn A. Let X = the number of green balls in Urn A after this process. List the possible values for X and then find the entire probability distribution for X.

Answer 1

Probability of transferring green ball from urn A to urn B = 5/9

Probability of transferring red ball from urn A to urn B = 4/9

If green ball is transferred from urn A to urn B, urn B will have 4 green balls and 6 red balls

In this case , Probability of transferring green ball from urn B to urn A = 4/10

So the number of green balls in urn after this process will be 5 with a probability 5/9*4/10 = 2/9

Probability of transferring red ball from urn B to urn A = 6/10

So the number of green balls in urn after this process will be 4 with a probability 5/9*6/10 = 1/3

If red ball is transferred from urn A to urn B, urn B will have 3 green balls and 7 red balls

In this case , Probability of transferring green ball from urn B to urn A = 3/10

So the number of green balls in urn after this process will be 6 with a probability 4/9*3/10 = 2/15

Probability of transferring red ball from urn B to urn A = 7/10

So the number of green balls in urn after this process will be 5 with a probability 4/9*7/10 = 14/45

X can take values 4,5,6

P(X = 4) = 1/3

P(X = 5) = 2/9 + 14/45 = 8/15

P(X = 6) = 2/15

X	4	5	6
P(X = x)	1/3	8/15	2/15