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Chapter 3: Q12E (page 169)

Male nannies. In a survey conducted by the International Nanny Association (INA) and reported on the INA Web site (www.nanny.org), 4,176 nannies were placed in a job in a given year. Only 24 of the nannies placed were men. Find the probability that a randomly selected nanny placed during the last year is a male nanny (a “mannie”).

Short Answer

Expert verified

The probability that a randomly selected nanny is a male nanny is 0.0057.

Step by step solution

01

Step-by-Step SolutionStep 1: Probability

Probability refers to the chance of something happening. It is a mathematical branch that studies the occurrence of a random event. The value is given as a number ranging from 0 to 1. Probability has been created to forecast how probable occurrences are to occur. Probability relates to how something is likely to occur.

02

Identify the probability of a male nanny

Given that,

Total number of nannies = 4,176

Number of male nannies = 24

P(malenanny)=TotalnumberofnanniesNumberofmalenanny=244,176=0.0057

Hence, the probability that a randomly selected nanny is a male nanny is0.0057.

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Most popular questions from this chapter

Detecting traces of TNT.University of Florida researchersin the Department of Materials Science and Engineering have invented a technique to rapidly detect traces of TNT (Today, Spring 2005). The method, which involves shining a laser light on a potentially contaminated object, provides instantaneous results and gives no false positives. In this application, a false positive would occur if the laser light detects traces of TNT when, in fact, no TNT is actually present on the object. Let A be the event that the laser light detects traces of TNT. Let B be the event that the object contains no traces of TNT. The probability of a false positive is 0. Write this probability in terms of A and B using symbols such as∪,∩and |.

Social networking Web sites in the United Kingdom. In the United States, MySpace and Facebook are considered the two most popular social networking Websites. In the United Kingdom (UK), the competition for social networking is between MySpace and Bebo. According to Nielsen/ Net Ratings (April 2006), 4% of UK citizens visit MySpace, 3% visit Bebo, and 1% visit MySpace and Bebo.

a. Draw a Venn diagram to illustrate social networking sites in the United Kingdom.

b. Find the probability that a UK citizen visits either the MySpace or Bebo social networking site.

c. Use your answer to part b to find the probability that a UK citizen does not visit either social networking site.

Patient medical instruction sheets. Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing patients’ awareness of the problem is for physicians to provide patient medication instruction (PMI) sheets. The American Medical Association, however, has found that only 20% of the doctors who prescribe drugs frequently distribute PMI sheets to their patients. Assume that 20% of all patients receive the PMI sheet with their prescriptions and that 12% receive the PMI sheet and are hospitalized because of a drug-related problem. What is the probability that a person will be hospitalized for a drug-related problem given that the person received the PMI sheet?

Ownership of small businesses. According to the Journal of Business Venturing (Vol. 17, 2002), 27% of all small businesses owned by non-Hispanic whites nationwide are women-owned firms. If we select, at random, a small business owned by a non-Hispanic white, what is the probability that it is a male-owned firm?

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.
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