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Chapter 3: Q104SE (page 204)

Workers’ unscheduled absence survey. Each year CCH, Inc., a firm that provides human resources and employment law information, conducts a survey on absenteeism in the workplace. The latest CCH Unscheduled Absence Surveyfound that of all unscheduled work absences, 34% are due to “personal illness,” 22% for “family issues,” 18% for “personal needs,” 13% for “entitlement mentality,” and 13% due to “stress.” Consider a randomly selected employee who has an unscheduled work absence.

a. List the sample points for this experiment.

b. Assign reasonable probabilities to the sample points.

c. What is the probability that the absence is due to something other than “personal illness”?

Short Answer

Expert verified
  1. The sample points are PI, F, P and E.
  2. The probability are 0.390, 0.252, 0.206 and 0.149.
  3. The probability is 0.609

Step by step solution

01

Important formula

The formula for probability is P=favourableoutcomestotaloutcomes.

02

The sample points.

a)

The sample points are

Here PI=personal illness

F=family issue

P=personal needs

E=entitlement mentality.

Thus, the sample points are PI, F, P, E.

03

Step 3:The possible probabilities.

b)

P(PI)=0.340.87=0.391

P(F)=0.220.87=0.253

P(P)=0.180.87=0.207

P(E)=0.130.87=0.149

Hence, the probability is 0.391, 0.253, 0.207, and 0.149.

04

The probability that the absence is due to something other than “personal illness”.

c)

P(FandPandE)=0.22+0.18+0.130.87=0.609

Therefore, the probability is 0.609

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Most popular questions from this chapter

Inactive oil and gas structures. U.S. federal regulations require that operating companies clear all inactive offshore oil and gas structures within 1 year after production ceases. Researchers at the Louisiana State University Center for Energy Studies gathered data on both active and inactive oil and gas structures in the Gulf of Mexico (Oil & Gas Journal, Jan. 3, 2005). They discovered that the Gulf of Mexico has 2,175 active and 1,225 idle (inactive) structures. The following table breaks down these structures by type (caisson, well protector, or fixed platform). Consider the structure type and active status of one of these oil/gas structures.

Structure type

Caisson

Well protector

Fixed platform

Totals

Active

503

225

1447

2175

Inactive

598

177

450

1225

a. List the simple events for this experiment.

b. Assign reasonable probabilities to the simple events.

c. Find the probability that the structure is active.

d. Find the probability that the structure is a well protector.

e. Find the probability that the structure is an inactive caisson.

Random shuffling of songs on Spotify. Spotify is a music streaming service that offers both free and subscription options. Users can create playlists and choose to use Spotify’s random shuffling feature to play back the songs. When the shuffling feature was first introduced, many users complained that the algorithm was not working. For example, in a playlist consisting of 2 songs by The White Stripes, 2 by Adele, and 1 by Maroon Five, two possible random orderings of the songs are:

A = {Adele 1, Adele 2, White Stripes 1, White Stripes 2, Maroon Five}

B = {Adele 2, White Stripes 1, Maroon Five, White Stripes 2, Adele 1}

  1. Find the probability that Adele 1 is selected as the first song to play from the playlist.
  2. Given that Adele 1 is selected as the first song, what is the probability that Adele 2 is selected as the second song to play from the playlist?
  3. Given that Adele 1 and Adele 2 are the first two songs selected, what is the probability that White Stripes 1 is selected as the third song to play from the playlist?
  4. Given that Adele 1, Adele 2, and White Stripes 1 are the first three songs selected, what is the probability that White Stripes 2 is selected as the fourth song to play from the playlist?
  5. Given that Adele 1, Adele 2, White Stripes 1 and White Stripes 2 are the first four songs selected, what is the probability that Maroon Five is selected as the last song to play from the playlist?
  6. Find the probability of List A by multiplying the probabilities in parts a–e.
  7. Many users considered List B to be random, but not List A. Demonstrate that the probability of List B is the same as the probability of List A. [Note: In response to user complaints, Spotify now uses a different random shuffling algorithm, one that prevents an outcome like List A from occurring.]

Ranking razor blades.The corporations in the highly competitive razor blade industry do a tremendous amount of advertising each year. Corporation G gave a supply of three top-name brands, G, S, and W, to a consumer and asked her to use them and rank them in order of preference.

The corporation was, of course, hoping the consumer would prefer its brand and rank it first, thereby giving them some material for a consumer interview advertising campaign. If the consumer did not prefer one blade over any other but was still required to rank the blades, what is the probability that

a.The consumer ranked brand G first?

b.The consumer ranked brand G last?

c.The consumer ranked brand G last and brand W second?

d.The consumer ranked brand W first, brand G second, and brand S third?

“Let’s Make a Deal.”Marilyn vos Savant, who is listedin Guinness Book of World Records Hall of Fame for“Highest IQ,” writes a weekly column in the Sunday newspaper supplement Parade Magazine. Her column, “AskMarilyn,” is devoted to games of skill, puzzles, and mind-bendingriddles. In one issue (Parade Magazine, February 24, 1991), vos Savant posed the following question:

Suppose you’re on a game show, and you’re given a choice of three doors. Behind one door is a car; behind the others, goats. You pick a door—say, #1—and the host, who knows what’s behind the doors, opens another door—say #3—which has a goat. He then says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice?

Marilyn’s answer: “Yes, you should switch. The first door has a 13 chance of winning [the car], but the second has a 23 chance [of winning the car].” Predictably, vos Savant’s surprising answer elicited thousands of criticalletters, many of them from PhD mathematicians, who disagreed with her. Who is correct, the PhDs or Marilyn?

Randomization in a study of TV commercials. Gonzaga University professors conducted a study of more than 1,500 television commercials and published their results in the Journal of Sociology, Social Work, and Social Welfare (Vol. 2, 2008). Commercials from eight networks—ABC, FAM, FOX, MTV, ESPN, CBS, CNN, and NBC—were sampled for 8 days, with one network randomly selected each day. The table below shows the actual order determined by random draw:

ABC—July 6 (Wed)

FAM—July 7 (Thr)

FOX—July 9 (Sat)

MTV—July 10 (Sun)

ESPN—July 11 (Mon)

CBS—July 12 (Tue)

CNN—July 16 (Sat)

NBC—July 17 (Sun)

a. What is the probability that ESPN was selected on Monday, July 11?

b. Consider the four networks chosen for the weekends (Saturday and Sunday). How many ways could the researchers select four networks from the eight for the weekend analysis of commercials? (Assume that the assignment order for the four weekend days was immaterial to the analysis.)

c. Knowing that the networks were selected at random, what is the probability that ESPN was one of the four networks selected for the weekend analysis of commercials?
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