4.11 Probability topics: homework  (Page 4/6)

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 64 stamped, addressed envelopes with $10 cash in different classrooms on the George Washington campus. 44% were returned overall. From the economics classes 56% of the envelopes were returned. From the business, psychology, and history classes 31% were returned. ( Source: Wall Street Journal )

Let: $R$ = money returned; $E$ = economics classes; $O$ = other classes

• a Write a probability statement for the overall percent of money returned.
• b Write a probability statement for the percent of money returned out of the economics classes.
• c Write a probability statement for the percent of money returned out of the other classes.
• d Is money being returned independent of the class? Justify your answer numerically and explain it.
• e Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

The chart below gives the number of suicides estimated in the U.S. for a recent year by age, race (black and white), and sex. We are interested in possible relationships between age, race, and sex. We will let suicide victims be our population. ( Source: The National Center for Health Statistics, U.S. Dept. of Health and Human Services )

• a Fill in the column for the suicides for individuals over age 64.
• b Fill in the row for all other races.
• c Find the probability that a randomly selected individual was a white male.
• d Find the probability that a randomly selected individual was a black female.
• e Find the probability that a randomly selected individual was black
• f Find the probability that a randomly selected individual was male.
• g Out of the individuals over age 64, find the probability that a randomly selected individual was a black or white male.
• h Comparing “Race and Sex” to “Age,” which two groups are mutually exclusive? How do you know?
• i Are being male and committing suicide over age 64 independent events? How do you know?

Complete the following:

• a Construct a table or a tree diagram of the situation.
• b $\text{P(driver is female)}$ =
• c $\text{P(driver is age 65 or over | driver is female)}$ =
• d $\text{P(driver is age 65 or over AND female)}$ =
• e In words, explain the difference between the probabilities in part (c) and part (d).
• f $\text{P(driver is age 65 or over)}$ =
• g Are being age 65 or over and being female mutually exclusive events? How do you know