A vase U1 contains 2 white balls, a vase U2 contains 2 red balls, a vase...

A vase U1 contains 2 white balls, a vase U2 contains 2 red balls, a vase U3 contains 2 white balls and 2 red balls and vase U4 contains 3 white balls and 1 red ball. The probability of choosing vase U1, U2, U3, and U4 are respectively 1/2, 1/4, 1/8 and 1/8. A vase is chosen and we retrieve the ball inside. Determine

a) The probability that the retrieved ball is white

b) Knowing the retrieved ball is white what is the probability that the ball was retrieved from vase U3.

Solutions

Expert Solution

The probability of choosing a ball is split in two parts. The first part depends on the urn and the second part depends on the colour of the ball.

Therefore the probability of a ball chosen = P( Urn) * P(colour)

a) The probability that the retrieved ball is white

White ball are only present in U1, U3, U4.

The probability of white being chosen = (Total white balls) / (total balls)

Urn	P(Urn) : A	No. of white balls	Total Balls	P(White chosen) :B	Probability (A * B)
1	1/2	2	2	2/2 = 1	1/2
3	1/8	2	2W+2R=4	2/4 = 1/2	1/16
4	1/8	3	3W+1R=4	3/4	3/32

Since there are three possibilities of white being chosen

Probability = 1/2 + 1/16 + 3/32

b) Knowing the retrieved ball is white what is the probability that the ball was retrieved from vase U3.

This is a case of conditonal probability. We want to find the probability that the ball is chosen from U3 given that (it is known that) it is a white ball. That mean out of probability of choosing white ball what is the probability of choosing from U3.

orchestra answered 2 years ago

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