FORMULABANK

Sometimes it is necessary to find the probability of an event where two outcomes are related.

Example

A spinning wheel has three fields (blue, red, and green). The fields are of equal size, which means that it is a uniform sample space.

What is the probability that the wheel stops on blue twice in a row?

Here we can say that the probability of landing on blue in the first round is $\frac{1}{3}$. The probability of landing on blue in the second round is also $\frac{1}{3}$. Since the wheel must land on blue in both the first and the second round, these two probabilities must be multiplied.

Thus, the calculation becomes: $\frac{1}{3}·\frac{1}{3}=\frac{1}{9}$

The probability is therefore $\frac{1}{9}$ for the wheel to land on blue two times in a row.