Question

Urn I contains five red chips and three white chips; urn II contains four reds and five whites. One chip is drawn at random from urn I and transferred to urn II. Then one chip is drawn from urn II. Suppose that a red chip is selected from urn II. What is the probability that the chip transferred was white?

Answer 1

Let

R1,W1 represent red and white chips from URN 1

R2,W2, represent red and white chips from URN 2

So

Urn1

5red and 3white

Urn 2

4red 5 white

So

Probability of red chip transfer from urn 1 to urn 2

=P(R1)=5/8

Probability of white chip transfer from urn 1 to urn 2

=P(W1)=3/8

Now

Probability of draw red chip from urn second when red chip is transferred from urn to urn 2

=P(R2|R1)=5/10

Probability of draw red chip from urn 2 when white chip is transferred from urn1 to urn 2

=P(R2|W1)=4/10

Now we have to find

P(W1|R2)=?

Now

Using Bayes rule

=0.15/0.4625=0.3243