Question

Each salesperson at an insurance agency is rated either below average, average, or above
average with respect to sales ability. Each salesperson is also rated with respect to his or her
potential for advancement either fair, good, or excellent. These traits for the 500 sales people
were cross-classified into the following table.
Potential for Advancement
Sales Ability Fair Good Excellent Total
Below Average 16 12 22 50
Average 45 60 45 150
Above Average 93 72 135 300
Total 154 144 202 500
If a salesperson is selected at random what is the probability:
A. The salesperson has “Fair” potential for advancement.
B. The salesperson has “Fair” potential or has Above Average Sales ability
C. The salesperson has “Fair” potential given they have Above Average Sales ability.
D. Of selecting 2 salespersons and finding they both have Fair potential for advancement.

Answer 1

Probability that the salesperson has “Fair” potential or has Above Average Sales ability is; 90.8%

How to find the probability?

A) Probability that the salesperson has “Fair” potential for advancement = (16 + 45 + 93)/500 = 154/500 = 30.8%

B)  Probability that the salesperson has “Fair” potential or has Above Average Sales ability = 30.8% + (300/500)% = 90.8%

C) Probability that the salesperson has “Fair” potential given they have Above Average Sales ability = P(A|B) = P(A ∩ B)/P(B) = (93/500)/0.6 = 0.31 = 31%

D) P(selecting 2 salespersons and finding they both have Fair potential for advancement) = (154/500) * (153/499) = 9.44%

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