Probability theory predicts that there is a 9% chance of a water polo team winning any particular match. if the water polo team playing two matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?

a. 8281
b. 1638
c. 81
d. 819

The result is B. 1638.

To calculate this, we will use both an addition and a multiplication rule. The addition rule is used to calculate the probability of one of the events from multiple pathways. If you want that only one of the events happens, you will use the addition rule. The multiplication rule calculates the probability that both of two events will occur.
First, there are two possibilities for winning exactly one match:
1. To win the first match and lose the second one.
2. To lose the first match and win the second one.

9% = 0.09 is the probability of winning. The probability of losing is 1-0.09 = 0.91. To calculate the probability of winning the first match and losing the second one and vice versa, we will use the multiplication rule:
1. 0.09 × 0.91 = 0.0819
2. 0.91 × 0.09 = 0.0819

We want to either one of these events to happen, so using the addition rule, we have:
0.0819 + 0.0819 = 0.1638

In 10,000 matches:
0.1638 × 10,000 = 1,638