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 at least 7 employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Total employee = 9( over 50 ) + 16 ( under 50 ) = 25

8 employees are dismissed.

Total number of ways to select 8 employees from 25 is ,

           { Using excel,   =COMBIN(25,8) = 1081575 }

We have to find P( at least 7 employees were over 50 ).

At least 7 means 7 or more than 7

There are two possible cases.

1) 7 employees over 50 and 1 employee under 50

2) All dismissed ( 8) employees are over 50

Number of ways for first case is ,

Number of ways for second case is ,

Total number of ways to select at least 7 employees were over 50 = 576 + 9 = 585

So , P( at least 7 employees were over 50 ) = 585 / 1081575 = 0.0005