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Chapter 3: Q96E (page 203)
For two events A and B, suppose ,,Find.
The value of is 0.8.
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Museum management. Refer to the Museum Management and Curatorship (June 2010) study of the criteria used to evaluate museum performance, Exercise 2.14 (p. 74). Recall that the managers of 30 leading museums of contemporary art were asked to provide the performance measure used most often. A summary of the results is reproduced in the table. Performance Measure Number of Museums Total visitors 8 Paying visitors 5 Big shows 6 Funds raised 7 Members 4
Performance Measure | Number of Museums |
Total visitors | 8 |
Paying visitors | 5 |
Big shows | 6 |
Funds raised | 7 |
Members | 4 |
a. If one of the 30 museums is selected at random, what is the probability that the museum uses total visitors or funds raised most often as a performance measure?
b. Consider two museums of contemporary art randomly selected from all such museums. Of interest is whether or not the museums use total visitors or funds raised most often as a performance measure. Use a tree diagram to aid in listing the sample points for this problem.
c. Assign reasonable probabilities to the sample points of part b.
d. Refer to parts b and c. Find the probability that both museums use total visitors or funds raised most often as a performance measure.
3 Paying monthly bills online. Do most people pay their monthly bills online? ABA Bank Marketing and Sales (July-August 2015) reported that 37% of U.S. customers pay their bills online using a personal computer. The table lists the different methods by which customers pay their monthly bills and associated probabilities. Consider the following two events:
A = {Customer does not pay monthly bills online.}
B = {Customer does not pay monthly bills with a credit or debit card.}
Payment Method | Probability |
Online via personal computer | .37 |
Write check | .22 |
Checking account withdrawal | .10 |
Debit card | .09 |
Credit card | .07 |
Cash | .08 |
Mobile bill account | .04 |
Online via tablet or e-reader | .03 |
a. Find .
b. Find.
c. Find .
d. Use the additive law of probability to find .
A pair of fair dice is tossed. Define the following events:
A: [Exactly one of the dice shows a 1.]
B: [The sum of the numbers on the two dice is even.]
a. Identify the sample points in the events
b. Find the probabilities of all the events from part a by summing the probabilities of the appropriate sample points.
C. Using your result from part b, explain why A and B are not mutually exclusive.
d. Find using the additive rule. Is your answer the same as in part b?
Compute each of the following:
a.
b.
c.
d.
e.
Firefighter glove sizing. Human Factors (December 2015) published a study on how well firefighter gloves fit. In a group of 586 firefighters who reported their glove size, the researchers determined whether the gloves fit well or poorly by gender. The data are summarized in the accompanying table. Consider the gender and glove fit status of a randomly selected firefighter.
a. List the sample points for this experiment.
b. Assign reasonable probabilities to these sample points.
c. Find the probability the firefighter is a female.
d. Find the probability the glove fits well.
e. Find the probability the firefighter is a female and has a well-fitting glove.
f. Find the probability the firefighter is a female or has a well-fitting glove.
Glove Fits Well | Glove Fits Poorly | Totals | |
Males | 415 | 132 | 547 |
Females | 19 | 50 | 39 |
Totals | 434 | 152 | 586 |
Source: H. Hsiao, et al., “Firefighter Hand Anthropometry and Structural Glove Sizing: A New Perspective,” Human Factors, Vol. 57, No. 8, December 2015 (Table 6).
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