EXAMPLE 23 Multiplication Rule for two independent events

Successive spins of the roulette wheel are independent because the wheel does not remember its result from the previous spin. Suppose the experiment is to spin the roulette wheel two times and to bet on red each time. There are 18 red numbers out of a total of 38 num-bers on the wheel. What is the probability that red will occur twice in succession?

Solution

Define the following events:

We have the probability of each event given as:

Then, because the successive spins are independent, the Multiplication Rule for Two Independent Events tells us: