Example

1. Example According to Current Population Reports, published by the Census Bureau, 52% of all US adults are female, 9.5% of US adults are divorced, and 5.4% of US adults are divorced females. For a US adult selected at random, let F represent the event that the person is female and let D represent the event that the person is divorced. From the information given, what is P(F), P(D), and P(F and D)? What is the probability that a person selected at random is either female or divorced? What is the probability that a randomly selected adult is male?

2. Example According to the Census Bureau, 12.6% of US residents are African-American and 6.6% are African-American women. What percentage of African-Americans are also women?

3. Example Consider the following table summarizing the results from tests for marijuana use: What is the probability that an individual either used marijuana or tested positive?

4. Example • A sprinkler system inside an office building has two types of activation devices, D1 and D2, which operate independently. When there is a fire, if either device operates correctly, the sprinkler system is turned on. In case of fire, the probability that D1 operates correctly is 0.95 and the probability that D2 operates correctly is 0.92. Find the probability that • Both D1 and D2 will operate correctly • The sprinkler system will come on • The sprinkler system will fail