Question

The Dilbert Investment Group employs 100 brokers. Twenty have been there less than 4 years, 50 have been there 4-8 years, and the rest have been there more than 8 years. A survey was distributed which asked brokers if they were Well Compensated, Fairly Compensated, or Poorly Compensated. Of the 20 brokers that were there less than four years; 8 said Well Compensated, 7 said Fairly Compensated and 5 said Poorly Compensated. Of the 50 there 4-8 years; the responses were 18, 20 and 12 respectively. Those there more than 8 years had responses of 8, 12 and 10 respectively.

a.) Develop a contingency table for the data.

b.) Find the probability that two brokers selected at random were both there less than 4 years.

c.) Find the probability that a broker said Fairly Compensated if there more than 8 years.

d.) Find the probability that a randomly selected broker said Well Compensated.

Answer 1

a)

The following table gives the contingency table for the data by summarizing the given details.

Compensation \ Experience	< 4 years	4 - 8 years	> 8 years	Total
Well compensated	8	18	8	34
Fairly compensated	7	20	12	39
Poorly compensated	5	12	10	27
Total	20	50	30	100

b)

The probability that two brokers selected at random were both there less than 4 years is given as

As there are 20 brokers with less than 4 years experience in total and so the probability that the first broker is of less than 4 years experience is (20 / 100) and the probability that the second broker is also having less than 4 years of experience is (19 / 99) since now only 19 out of 99 brokers left. The entire probability is the product of these two probabilities as the events are independent.

c)

The probability that a broker said Fairly compensated if there more than 8 years is the ratio between the number of brokers with more than 8 years experience and said fairly compensated to the total number of brokers.

d)

The probability that a randomly selected broker said Well compensated is the ratio between the total number of brokers said well compensated and the total number of brokers.