Urn 1 contains 2 white and 1 black ball Urn 2 contains 4 whi

Urn 1 contains 2 white and 1 black ball. Urn 2 contains 4 white and 5 black ball. A ball is drawn from urn 1 and placed in urn 2. What is the probability that the ball drawn from urn 1 was white given that the ball drawn from urn 2 is white ? 1/2 3/5 2/3 5/7 0.72

Solution

A: white ball transfferred from 1 to 2

B: black ball transferred form 1 to 2

C: the ball is white

P(C)=P(A).P(C/A)+P(B)*P(B/A)

P(A)=2/3

P(B)=1/3

P(C/A)=getting white ball after it is transffered to 2=5/10

P(B/A)= gettig black ball when transffered is white =5/10

P(C)=2/3*5/10+1/3*5/10=10/30+5/30=15/30=1/2