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Chapter 3: Q94SE (page 203)

Which of the following pairs of events are mutually exclusive? Justify your response.

  1. {The next customer entering a retail store is older than 30 years.}, {The next customer entering the same retail store is younger than 20 years.}
  2. {The next customer entering a retail store is younger than 20 years.}, {The next customer entering the same retail store will spend more than \(900 in purchases.}
  3. {The next customer entering the retail store will be older than 70 years and spend more than \)900 in purchases.}, {The next customer entering the same retail store will try to steal an item.}

Short Answer

Expert verified
  1. Both events are not mutually exclusive.
  2. Both events are mutually exclusive.
  3. Both events are mutually exclusive.

Step by step solution

01

Important definition

The two events are called mutually exclusive if P(A∩B)=0.

02

Solution for part (a)

It is possible that the data scheduled above will actually occur and is not mutually exclusive events.

03

Find the result for part (b)

It is impossible for all of the occurrences to happen immediately and these are mutually exclusive events.

04

Determine the result for part (c)

It is impossible for all of the occurrences to happen immediately and these are mutually exclusive events.

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Most popular questions from this chapter

Jai-alai bets. The Quinella bet at the paramutual game of jai-alai consists of picking the jai-alai players that will place first and second in a game irrespective of order. In jai-alai, eight players (numbered 1, 2, 3, . . . , 8) compete in every game.

a. How many different Quinella bets are possible?

b. Suppose you bet the Quinella combination of 2—7. If the players are of equal ability, what is the probability that you win the bet?

Suppose the events B1and B2are mutually exclusive and complementary events, such thatP(B1)=.75andP(B2)=.25 Consider another event A such that role="math" localid="1658212959871" P(AB1)=.3, role="math" localid="1658213029408" P(AB2)=.5.

  1. FindP(B1∩A).
  2. FindP(B2∩A)
  3. Find P(A) using part a and b.
  4. Findrole="math" localid="1658213127512" P(B1A).
  5. Findrole="math" localid="1658213164846" P(B2A).

World’s largest public companies. Forbes (May 6, 2015) surveyed the 20 largest public companies in the world. Of these 20 companies, 4 were banking or investment companies based in the United States. A total of 9 U.S. companies were on the top 20 list. Suppose we select one of these 20 companies at random. Given that the company is based in the United States, what is the probability that it is a banking or investment company?

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?

Condition of public school facilities. The National Center for Education Statistics (NCES) conducted a survey on the condition of America’s public school facilities. The survey revealed the following information. The probability that a public school building has inadequate plumbing is .25. Of the buildings with inadequate plumbing, the probability that the school has plans for repairing the building is .38. Find the probability that a public school building has inadequate plumbing and will be repaired.
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