## Related questions with answers

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

VerifiedGiven: 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

$A_1$=Red chip is drawn is from Urn I and Red chip is drawn from Urn II

$A_2$=Red chip is drawn is from Urn I and White chip is drawn from Urn II

$A_3$=White chip is drawn is from Urn I and Red chip is drawn from Urn II

$A_4$=White chip is drawn is from Urn I and white chip is drawn from Urn II

$B$=Second draw is red.

Result theorem of this section:

$P(B)=\sum_{i=1}^n P(B|A_i)P(A_i)$

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