Question

A recent survey reported in Bloomberg Businessweek dealt with the salaries of CEOs at large corporations and whether company shareholders made money or lost money.

	CEO Made More Than				CEO Made Less Than
	$1 Million				$1 Million				Total
Shareholders made money		2				14				16
Shareholders lost money		8				6				14
Total		10				20				30

  

If a company is randomly selected from the list of 30 studied, what is the probability:

1. The CEO made more than $1 million? (Round your answer to 2 decimal places.)

2. The CEO made more than $1 million or the shareholders lost money? (Round your answer to 2 decimal places.)

3. The CEO made more than $1 million given the shareholders lost money? (Round your answer to 4 decimal places.)

4. Of selecting two CEOs and finding they both made more than $1 million? (Round your answer to 4 decimal places.)

Answer 1

a). Prob.(CEO made more than 1 million) = 10/30 = 0.3333, or 33.33%

b). Prob.(CEO made more than 1 million OR shareholders lost money)

= prob(CEO >1 million) + prob(shareholders lost) - prob(CEO > 1 million)AND(shareholders lost)

= (10 / 30) + (14 / 30) - (8 / 30) = 16 / 30 = 0.5333, or 53.33%

c). Prob.(CEO made more than $1 million given the shareholders lost money)

= probability (CEO > 1 million) / (shareholders lost) = 8 / 14= 0.571429, or 57.1429%

d). 10/30 made over 1 million, then 9 are left after one is already selected (cannot select same person twice since question D was worded as "both more than 1 million")

Prob.(Of selecting 2 CEO independently, with both making over 1 million)

= (10 / 30) x (9 / 29) = 0.103448, or 10.3448%5