Q. 125.0( 2 Votes )

Suppose we have four boxes A,B,C,D containing coloured marbles as given below:



One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn form box A? box B? box C?

Answer :

Let us assume U1, U2, U3, U4 and A be the events as follows:


U1 = choosing Box A


U2 = choosing Box B


U3 = choosing Box C


U4 = choosing Box D


A = choosing red marble from box


We know that each box is most likely to choose. So, probability of choosing a box will be same for every Urn.






The Probability of choosing marble from each box differs from box to box and the probabilities are as follows:


P(A|U1) = P(Choosing red marble from Box A)





P(A|U2) = P(Choosing red marble from Box B)





P(A|U3) = P(Choosing red marble from Box C)





Since there is no red marbles in Box D, the probability of choosing red marble is 0.


i.e, P(A|U4) = 0


Now we find


P(U1|A) = P(The chosen red marble is from Box A)


P(U2|A) = P(The chosen red marble is from Box B)


P(U3|A) = P(The chosen red marble is from Box C)


Using Baye’s theorem:














The required probabilities are .

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