Question

SECOND TIME POSTING THIS QUESTION PLEASE DON'T GIVE ANSWER AS A PERCENTAGE

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

Number of ways in which r items can be selected from n, nCr = n!/(r! x (n-r)!)

P(no more than 1 employee was over 50) = P(0 employees are over 50) + P(1 employee is over 50)

= (Number of ways to select 8 employees from 16 employees that are under 50 / Number of ways to select 8 employees from total 25) + (Number of ways to select 7 employees from 16 employees that are under 50 x Number of ways to select 1 employee from 9 that are over 50 / Number of ways to select 8 employees from total 25)

= 16C8/25C8 + 16C7x9C1/25C8

= (16C8 + 16C7x9)/25C8

= (12870 + 11,440x9)/1,081,575

= 0.1071