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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.
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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
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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. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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