There are four boxes, A,B,C and D, containing marbles. A contains 1 red, 6 white and 3 black marbles; B contains 6 red, 2 white and 2 black marbles; C contains 8 red, 1 white and 1 black marbles; and D contains 6 white and 4 black marbles. One of the boxes is selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from the box A?
Let A : Ball drawn from bag A
B : Ball is drawn from bag B
C : Ball is drawn from bag C
D : Ball is drawn from bag D
BB : Black ball
WB : White ball
RB : Red ball
Assuming all boxes have an equal probability for picking i.e.
We want to find P(A|RB), i.e. probability of selected red ball is from box A
Conclusion: Therefore, the probability of selected red ball is from box A is