Urn 1 contains three red chips and one white chip. Urn 2 contains two red chips

Question

Urn 1 contains three red chips and one white chip. Urn 2 contains two red chips and two white chips. One chip is drawn from each urn and transferred to the other urn. Then a chip is drawn from the urn. What is the probability that the chip ultimately drawn from urn 1 is red? Urn 1 contains three red chips and one white chip. Urn 2 contains two red chips and two white chips. One chip is drawn from each urn and transferred to the other urn. Then a chip is drawn from the urn. What is the probability that the chip ultimately drawn from urn 1 is red?

Explanation / Answer

Here there could be 4 cases.

Therefore the probability distribution for the number of red balls in Urn 1 would be written as:

P(X=2) = 0.375, P(X=3) = 0.125 + 0.375 = 0.5, and P(X=4) = 0.125

Now probability that a red ball would be drawn from Urn 1 would be computed as:

= 0.5*0.375 + 0.75*0.125 + 1*0.125

= 0.40625

Therefore 0.40625 is the required probability here.

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