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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

  • Write a probability statement for the overall percent of money returned.
  • Write a probability statement for the percent of money returned out of the economics classes.
  • Write a probability statement for the percent of money returned out of the other classes.
  • Is money being returned independent of the class? Justify your answer numerically and explain it.
  • 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 )

Race and Sex 1 - 14 15 - 24 25 - 64 over 64 TOTALS
white, male 210 3360 13,610 22,050
white, female 80 580 3380 4930
black, male 10 460 1060 1670
black, female 0 40 270 330
all others
TOTALS 310 4650 18,780 29,760
Do not include "all others" for parts (f), (g), and (i).
  • Fill in the column for the suicides for individuals over age 64.
  • Fill in the row for all other races.
  • Find the probability that a randomly selected individual was a white male.
  • Find the probability that a randomly selected individual was a black female.
  • Find the probability that a randomly selected individual was black
  • Find the probability that a randomly selected individual was male.
  • Out of the individuals over age 64, find the probability that a randomly selected individual was a black or white male.
  • Comparing “Race and Sex” to “Age,” which two groups are mutually exclusive? How do you know?
  • Are being male and committing suicide over age 64 independent events? How do you know?
  • 22050 29760 size 12{ { {"22050"} over {"29760"} } } {}
  • 330 29760 size 12{ { {"330"} over {"29760"} } } {}
  • 2000 29760 size 12{ { { size 8{"2000"} } over { size 8{"29760"} } } } {}
  • 23720 29760 size 12{ { { size 8{"23720"} } over { size 8{"29760"} } } } {}
  • 5010 6020 size 12{ { { size 8{"5010"} } over { size 8{"6020"} } } } {}
  • Black females and ages 1-14
  • No

The next two questions refer to the following: The percent of licensed U.S. drivers (from a recent year) that are female is 48.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20 - 64; 13.61% are age 65 or over. Of the licensed U.S. male drivers, 5.04% are age 19 and under; 81.43% are age 20 - 64; 13.53% are age 65 or over. (Source: Federal Highway Administration, U.S. Dept. of Transportation)

Complete the following:

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

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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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