Question

# Urn A contains 5 green and 4 red balls, and Urn B contains 3 green and...

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.

Solution:

Case 1: transfer a green ball from A to B and then transfer a green from B to A . then X= 5

P(case1) = 5/9 * 4/10 * 5/9= 0.12

Case 2: transfer a green ball from A to B and then transfer a Red from B to A . then X= 4

P(case 2) = 5/9 * 6/10 * 4/9 = 0.15

Case 3 : transfer a red ball from A to B and then transfer a red from B to A . then X= 5

P( case 3) = 4/9 * 7/10 * 5/9 = 0.17

Case 4: transfer a red ball from A to B and then transfer a green from B to A . then X= 6

P(case 4) = 4/9 * 3/10 * 6/9 = 0.09

So probability distribution

 X p(x) 4 0.15 5 0.12 + 0.17= 0.29 6 0.09

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