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?

Question

Philoid · Accepted 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.

&rArr;

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

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

&rArr;

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

&rArr;

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

&rArr;

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&rsquo;s theorem:

&rArr;

&there4; The required probabilities are .

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?