Question

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

1. 0.425
2. 0.361

Step-by-step solution

 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

$\begin{array}{c}\text{P=}\frac{\text{A}}{\text{B}}\\ \text{=}\frac{\text{17}}{\text{40}}\\ \text{=0.425}\end{array}$

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

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 5^th CEO also has a bachelor’s degree will be o.361.

$\begin{array}{c}\text{P=}\frac{\text{A}}{\text{B}}\\ \text{=}\frac{\text{13}}{\text{36}}\\ \text{=0.361}\end{array}$