Made money
Lost money
Total
CEO More than $1M
2
4
6
CEO Less than $1M
11
3
14
Total
13
7
20
66. A recent survey reported in BusinessWeek dealt with the salaries of CEOs at large
corporations and whether company shareholders made money or lost money. CEO Paid More
than 1 million CEO Paid Less than 1 million Total Shareholders made money 2 11 13
Shareholders lost money 6 14 20 Total 6 14 20 If a company is randomly selected from the list
of 20 studied, what is the probability: a. the CEO made more than $1 million? b. the CEO made
more than $1 million or the shareholders lost money? c. the CEO made more than $1 million
given the shareholders lost money? d. of selecting 2 CEOs and finding they both made more
than $1 million?
a. All CEOs who made more than $1M / All companies
6/20 = 0.3
b. Probability of the CEO making more than $1M is 6/20
Probability of the shareholder losing money is 7/20
Add them together and get 13/20
BUT we have to subtract the companies where both things are true, because they were
counted in both groups.
13/20 – 4/20 = 9/20 = 0.45
(Another way to think about this is that the ONLY group where neither of these things
are true, is the 11 companies where the CEO makes less than $1M AND the
shareholders made money. So we can subtract the probability of that, 11/20 from 1.
And get 9/20, which is the solution we came up with the other way).
c.
This time we are only looking at the “lost money” row because that’s given.
So the probability that the CEO made more than $1M is 4/7 = 0.5714
d.
The chance of finding that the first CEO makes more than $1M is 6/20
The chance that the second CEO makes more than $1M is 5/19
Multiply the two probabilities together and get 30/380 = 0.0789