Question

Urn A contains 6 green and 4 red balls, and Urn B contains 3 green and 7 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

number of green balls in Urn can take values from 5 to 7 (as there can be a sift of at most one ball from original content)

possible values for X are 5,6,7

probability distribution for X is as follows:

P(X=5)=P(green from urn A to b and red from urn B to A) =(6/10)*(7/11)=21/55

P(X=6)=(P(green from urn A to b and green from urn B to A)+(P(red from urn A to b and red from urn B to A)

=(6/10)*(4/11)+(4/10)*(8/11)=28/55

P(X=7)=P(ed from A to B and green from B to A) =(4/10)*(3/11)=6/55