5.2 - Three Theorems

On this page, we present, prove, and then use three sometimes helpful theorems.

Example 5-5 Section

pizza

A nationwide poll determines that 72% of the American population loves eating pizza. If two people are randomly selected from the population, what is the probability that the first person loves eating pizza, while the second one does not?

Answer

Let \(A\) be the event that the first person loves pizza, and let \(B\) be the event that the second person loves pizza. Because the two people are selected randomly from the population, it is reasonable to assume that \(A\) and \(B\) are independent events. If \(A\) and \(B\) are independent events, then \(A\) and \(B^\prime\) are also independent events. Therefore, \(P(A\cap B^\prime)\), the probability that the first person loves eating pizza, while the second one does not can be calculated by multiplying their individual probabilities together. That is, the probability that the first person loves eating pizza, while the second one does not is:

\(P(A\cap B^\prime)=0.72(1-0.72)=0.202\)