In: Statistics and Probability
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?
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