Question

A town recently dismissed 8 employees in order to meet their new budget reductions. The town had 9 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that no more than 1 employee was over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Total Dismissed employees = 8

Employees above 50 = 9

Employees below 50 = 16

Total Employees = 25

Total sample space = 25 C 8

If the dismissed employees were selected at random, there can be two cases here :

1. One employee over 50 was dismissed :

Total 8 employees are to be dismissed

1 from 9 employees above 50 is to be dismissed.

7 from 16 employees below 50 are to be dismissed

Probability that 1 employee above 50 was dismissed = 9C1 * 16C7 / 25C8 = 0.0951945 = 9.52%

2. None of the employees above 50 are dismissed:

Total 8 employees are to be dismissed

0 from 9 employees above 50 is to be dismissed.

8 from 16 employees below 50 are to be dismissed

Probability that 1 employee above 50 was dismissed = 9C0 * 16C8 / 25C8 = 0.0118993 = 1.19%

Therefore, Total Probability = 9.52% + 1.19% = 10.70938%

Therefore,  probability that no more than 1 employee was over 50 = 10.70938%