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Question

Urn I contains three red chips and one white chip. Urn II 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 first urn. What is the probability that the chip ultimately drawn from urn I is red?

Solution

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Given: Urn I contains 3 red chips and 1 white chip. Urn II contains 2 red chips and 2 white chips. The first drawn is from each urn and the chips are interchanged. The second draw is from Urn 1

A1A_1=Red chip is drawn is from Urn I and Red chip is drawn from Urn II

A2A_2=Red chip is drawn is from Urn I and White chip is drawn from Urn II

A3A_3=White chip is drawn is from Urn I and Red chip is drawn from Urn II

A4A_4=White chip is drawn is from Urn I and white chip is drawn from Urn II

BB=Second draw is red.

Result theorem of this section:

P(B)=i=1nP(BAi)P(Ai)P(B)=\sum_{i=1}^n P(B|A_i)P(A_i)

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