Question

A town recently dismissed 8 employees in order to meet their new budget reductions. The town had 5 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that exactly 1 employee was over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Answer

we have total 8 dismissed employees and total number of employees = 5+16 = 21

We have to select only 1 employee over 50 years and remaining 7 employees under 50 years

Using combination, number of ways of selecting 1 employee over 50 and 7 employees under 50, we can write it as

Number of ways = combination(n,r) + combination(N,R)

where n = 5, r = 1, N = 16 and R = 7

setting the values, we get

Number of ways = combination(5,1) * combination(16,7) =

(51/((5-1)! * 1!)) * (161/((16-7)! * 7!)) = 57200ways

So, possible number of ways in which exactly 1 employee was over 50

Total number of dismissing 8 employees out of 21 employees = combination(21,8) =

(21!// ( (21-8)! * S!))-203490

So, required probability = (number of dismissing exactly 1 employee over 50)/(total number of ways of dismissing 8 employee)

setting the values

we get

Required probability = (57200/203490)= 0.2811

So, the required probability that exactly 1 employee was over 50 is 0.2811