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Chapter 3: Q70E (page 195)

Degrees of best-paid CEOs.Refer to the results of the Glassdoor Economic Research (August 25, 2015) survey of the top 40 best-paid CEOs shown in Table 2.1 (p. 65). The data on the highest degree obtained are summarized in the SPSS printout below. Suppose you randomly select five of the CEOs (without replacement) and record the highest degree obtained by each.

a.What is the probability that the highest degree obtained by the first CEO you select is a bachelor’s degree?

b.Suppose the highest degree obtained by each of the first four CEOs you select is a bachelor’s degree. What is the probability that the highest degree obtained

by the fifth CEO you select is a bachelor’s degree?

Short Answer

Expert verified
  1. 0.425
  2. 0.361

Step by step solution

01

 Step 1: Finding the probability that the highest degree obtained by the first CEO you select is a bachelor’s degree

Let A be the number of CEOs with a bachelor’s degree

Let B be the total number of CEOs

P=AB=1740=0.425

Therefore, the probability that you randomly choose a CEO with a bachelor’s degree as the highest qualification is 0.425.

02

Computing the probability that you consecutively pick the 5th CEO again with a bachelor’s degree 

We select 5 CEOs without replacement. So once we have chosen 4 CEOs, the total number of CEOs reduces to 36 (40 – 4).

And if the 4 chosen CEOs have bachelors as the highest qualification, the number of CEOs with a bachelor’s degree will also fall to 13.

So now the probability that the 5th CEO also has a bachelor’s degree will be o.361.

P=AB=1336=0.361

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Most popular questions from this chapter

Most likely coin-tossing sequence. In Parade Magazine’s (November 26, 2000) column “Ask Marilyn,” the following question was posed: “I have just tossed a [balanced] coin 10 times, and I ask you to guess which of the following three sequences was the result. One (and only one) of the sequences is genuine.”

(1) H HHHHHHHHH

(2) H H T T H T T H HH

(3) T TTTTTTTTT

  1. Demonstrate that prior to actually tossing the coins, thethree sequences are equally likely to occur.
  2. Find the probability that the 10 coin tosses result in all heads or all tails.
  3. Find the probability that the 10 coin tosses result in a mix of heads and tails.
  4. Marilyn’s answer to the question posed was “Though the chances of the three specific sequences occurring randomly are equal . . . it’s reasonable for us to choose sequence (2) as the most likely genuine result.” If you know that only one of the three sequences actually occurred, explain why Marilyn’s answer is correct. [Hint: Compare the probabilities in parts b and c.]

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 A,B,A∩B,A∪B,andAc.

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 P(A∪B) using the additive rule. Is your answer the same as in part b?

Consider the Venn diagram in the next column, where

P(E1)=0.10,P(E2)=0.05,P(E3)=P(E4)=0.2,P(E5)=0.6,P(E6)=0.3,P(E7)=0.06andP(E8)=0.3

Find each of the following probabilities:

a.P(Ac)b.P(Bc)c.P(Ac∩B)d.P(A∪B)e.P(A∩B)f.P(Ac∩Bc)

g. Are events A and B mutually exclusive? Why?

Problems at major companies. The Organization Development Journal (Summer 2006) reported on a survey of human resource officers (HROs) at major employers. The focus of the study was employee behaviour, namely, absenteeism and turnover. The study found that 55% of the HROs had problems with employee absenteeism; 41% had problems with turnover. Suppose that 22% of the HROs had problems with both absenteeism and turnover. Use this information to find the probability that an HRO selected from the group surveyed had problems with either employee absenteeism or employee turnover.

Study of analysts' forecasts. The Journal of Accounting Research (March 2008) published a study on the relationship between incentives and the degree of optimism among analysts' forecasts. Participants were analysts at either a large or small brokerage firm who made their forecasts early or late in the quarter. Also, some analysts were only concerned with making an accurate forecast, while others were also interested in their relationship with management. Suppose one of these analysts is randomly selected.

Consider the following events:

A = {The analyst is concerned only with making an accurate forecast.}

B = {The analyst makes the forecast early in the quarter.}

C = {The analyst is from a small brokerage firm.}

Describe the following events in terms of unions, intersections, and complements (e.g.,A∪B,A∩B,Ac, etc.).

a. The analyst makes an early forecast and is concerned only with accuracy.

b. The analyst is not concerned only with accuracy.

c. The analyst is from a small brokerage firm or makes an early forecast.

d. The analyst makes a late forecast and is not concerned only with accuracy.
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