Solution for Problem 8.8.3

Suppose we pick 2 balls out of a box  with replacement. Let's say 8 are red and 6 are blue.
What is the probability of picking a red ball then a blue ball?

Solve

Step

Pick red first.  Pr(red) = 8/14

There are a total of 14 balls in the box.

Then pick blue.  Pr(blue) = 6/14

The number of balls is not reduced because the question said with replacement. The first ball is put back into the box.

Pr(red then blue) = 8/14 × 6/14 = 48/156 = 12/49

These events are independent