# Probability : Random Selection and Conditional Probability

12. Urn I contains 2 white and 4 red balls, whereas urn II contains 1 white and 1 red ball. A ball is randomly chosen form urn I and put into urn II, and a ball is then randomly selected from urn II. What is

(a) the probability that the ball selected from urn II is white;

(b) the conditional probability that the transferred ball was white, given that a white ball is selected from urn II?

https://brainmass.com/math/probability/probability-random-selection-conditional-probability-33652

#### Solution Preview

The answer of (a) is 4/9 and the answer of (b) is 8/9.

(a) When a ball is randomly chosen from urn I to urn II, it can be white or red. Because urn I contains 2 white balls and 4 red balls, the probability that the randomly-chosen ball from urn I is white is 2/(2+4)=1/3. In this ...

#### Solution Summary

A random selection probability problem is solved.

$2.19