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


1