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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鈥檚 degree?

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

by the fifth CEO you select is a bachelor鈥檚 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鈥檚 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鈥檚 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 鈥� 4).

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

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

P=AB=1336=0.361

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Most popular questions from this chapter

Confidence of feedback information for improving quality. In the semiconductor manufacturing industry, a key to improved quality is having confidence in the feedback generated by production equipment. A study of the confidence level of feedback information was published in Engineering Applications of Artificial Intelligence(Vol. 26, 2013). At any point in time during the production process, a report can be generated. The report is classified as either 鈥淥K鈥� or 鈥渘ot OK.鈥� Let Arepresent the event that an 鈥淥K鈥� report is generated in any time period (t).Let Brepresent the event that an 鈥淥K鈥� report is generated in the next time period. Consider the following probabilities:

P(A)=0.8,PBA=0.9, andPBAC=0.5.

a. Express the event B|Ain the words of the problem.

b. Express the event B|ACin the words of the problem.

c. FindP(AC).

d. FindP(A鈭�B).

e. FindP(AC鈭�B).

f. Use the probabilities, parts d and e, to find P(B).

g. Use Bayes鈥� Rule to find P(A|B), i.e., the probability that an 鈥淥K鈥� report was generated in one time period(t), given that an 鈥淥K鈥� report is generated in the next time period(t+1).

Two fair dice are tossed, and the following events are defined:

A: {Sum of the numbers showing is odd.}

B: {Sum of the numbers showing is 9, 11, or 12.}

Are events A and B independent? Why?

A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probabilities of the sample points are

P (1) = .20, P (2) = .05, P (3) = .30, P (4) = .10,P (5) = .10, P (6) = .25.

a. Which pairs of events, if any, are mutually exclusive? Why?

b. Which pairs of events, if any, are independent? Why?

c. FindP (A鈭�B) by adding the probability of the sample points and then using the additive rule. Verify that the answers agree. Repeat forP (A鈭�C)

Exit poll candidates and voters.In an exit poll, 45% of voters said that the main issue affecting their choice of candidates was the economy, 35% said national security, and the remaining 20% were not sure. Suppose we select one of the voters who participated in the exit poll at random and ask for the main issue affecting his or her choice of candidates.

  1. List the sample points for this experiment.
  2. Assign reasonable probabilities to the sample points.
  3. What is the probability that the main issue affecting randomly selected voters鈥� choice was either the economy or national security?

Three fair coins are tossed and either heads(H) or tails(T) are observed for each coin.

  1. List the sample points for the experiment.
  2. Assign probabilities to the sample points.
  3. Determine the probability of observing each of the following events:

A= {Three heads are observed}

B= {Exactly two heads are observed}

C= {At least two heads are observed}

See all solutions

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