In given problem, are the events "top executive made more than $1 million" and "shareholders lost money" independent of each other? If this is true for all firms, how would you interpret your finding?
Problem
The following table lists the number of firms where the top executive officer made over $1 million per year. The table also lists firms according to whether shareholder return was positive during the period in question.
|
|
Top executive made more than $1 Million
|
Top executive Made less than $1 Million
|
Total
|
|
Shareholders made money
|
1
|
6
|
7
|
|
Shareholders lost money
|
2
|
1
|
3
|
|
Total
|
3
|
7
|
10
|
a. If a firm is randomly chosen from the list of 10 firms studied, what is the probability that its top executive made over $1 million per year?
b. If a firm is randomly chosen from the list, what is the probability that its shareholders lost money during the period studied?
c. Given that one of the firms in this group had negative shareholder return, what is the probability that its top executive made over $1 million?
d. Given that a firm's top executive made over $1 million, what is the probability that the firm's shareholder return was positive?