Three urns A, B and C contains 6 red and 4 white; 2 red and 6 white; and 1 red and 5 white balls respectively. An urn is chosen at random, and a ball is drawn. If the ball drawn is found to be red, find the probability that the balls was drawn from the first urn A.
let A : Ball drawn from bag A
B : Ball is drawn from bag B
C : Ball is drawn from bag C
R : Red ball
W : White ball
Assuming, selecting bags is of equal probability i.e.
We want to find P(A|R), i.e. probability of selected red ball is from bag A
Conclusion: Therefore, the probability of selected red ball is from bag A is