Question

In: Statistics and Probability

There are two urns, urn I and urn II. Urn I contains 2 white balls and...

There are two urns, urn I and urn II. Urn I contains 2 white balls and 4 red balls, and urn II
contains 1 white ball and 1 red ball. A ball is randomly chosen from urn I and put into urn II,
and a ball is then randomly selected from urn II. What is the probability that the ball selected
from urn II is white?

Solutions

Expert Solution

Solution:

We are given that: There are two urns, urn I and urn II.

Urn I contains 2 white balls and 4 red balls,

2 White


4 Red
Total =6

Urn II contains 1 white ball and 1 red ball.

1 White


1 Red
Total =2

A ball is randomly chosen from urn I and put into urn II,
and a ball is then randomly selected from urn II.

We have to find the probability that: the ball selected from urn II is white?

Let Tw= Transferred ball is White Ball and Tr= Transferred ball is Red ball.

W = Ball selected from urn II is White.

Thus we have to find:

P(W) =..........?

P(W) = P(Tw) x P(W| Tw) + P(Tr) x P(W| Tr)

If Transferred ball is White Ball , then its probability is P(Tw)= 2/6 and then in urn II we have 2 white balls and 1 Red ball, thus total balls in urn II are 2 white + 1 red = 3 balls, thus P(W| Tw) = 2/3.

If Transferred ball is Red Ball , then its probability is P(Tr)= 4/6 and then in urn II we have 1 white ball and 2 red balls, thus total balls in urn II are 1 white + 2 red = 3 balls, thus P(W| Tr) = 1/3.

Thus


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