Urn1 contains 5 red and 4 white marbles. Urn2 contains 4 red and 5 white marbles

Question

Urn1 contains 5 red and 4 white marbles. Urn2 contains 4 red and 5 white marbles. two marbles are drawn without replacement from urn1 and trasfered to urn2. then a single marble is drawn from urn2. what is the probability that the single marble drawn from the urn2 is white? this problem is straightforward when broken into following steps:

(a)For 0 is lessthan or equal to i lessthan or equal to 2, Let Ai denote the event that i red marblems are transferred from urn1 to urn2. Compute P(A0), P(A1) P(A2)

(b)Let W denotes the event that the singlr marble drawn from urn2 is white. Compute P(W|A0), P(W|A1) and P(W|A2)

(c) USe the Law of Total Probabilty to compute P(W).

Explanation / Answer

Urn1----> 5R +4W

Urn2---->4R+5W

P(drawing white from Urn2)

a)P(A0)=4C2/9C2=1/6

P(A1)=5/9

P(A2)=5C2/9C2=5/18

b)5R+6W----->P(W|A0)=6/11

6R+5W-------->P(W|A1)=5/11

7R+4W------->P(W/A2)=4/11

c)P(W)=P(A0)P(W|A0)+P(A1)P(W|A1)+P(A2)P(W|A2)=4/9

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