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Chapter 3: 3 (page 168)
The sample space for an experiment contains five sample points with probabilities as shown in the table. Find the probability of each of the following events:
a. Either 1,2 or 3 occurs
b. Either 1,3 or 5 occurs
c. 4 does not occur
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Chance of an Avon sale.The probability that an Avon salesperson sells beauty products to a prospective customer on the first visit to the customer is .4. If the salesperson fails to make the sale on the first visit, the probability that the sale will be made on the second visit is .65. The salesperson never visits a prospective customer more than twice. What is the probability that the salesperson will make a sale to a particular customer?
The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The accompanying two-way table gives the probabilities associated with each of the six possible outcome pairs.
Low | Medium | High | |
On | .50 | .10 | .05 |
Off | .25 | .07 | .03 |
Consider the following events:
A: {On}
B: {Medium or on}
C: {Off and Low}
D: {High}
a. Find P (A).
b. Find P (B).
c. Find P (C).
d. Find P (D).
e. Find.
f. Find.
g. Find.
h. Consider each pair of events (A and B, A and C, A and D, B and C, B and D, C and D). List the pairs of events that are mutually exclusive. Justify your choices.
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.
Advertising proposals. The manager of an advertising department has asked her creative team to propose six new ideas for an advertising campaign for a major client. She will choose three of the six proposals to present to the client. The proposals were named A, B, C, D, E, and F, respectively.
a. In how many ways can the manager select the three proposals? List the possibilities.
b. It is unlikely that the manager will randomly select three of the six proposals, but if she does, what is the probability that she will select proposals A, D, and E?
Simulate the experiment described in Exercise 3.7 using any five identically shaped objects, two of which are one colour and the three another colour. Mix the objects, draw two, record the results, and then replace the objects. Repeat the experiment a large number of times (at least 100). Calculate the proportion of time events A, B, and C occur. How do these proportions compare with the probabilities you calculated in Exercise 3.7? Should these proportions equal the probabilities? Explain.
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