Question

t​ Technodynamics, Inc., a​ randomly-selected hiring committee of 3 people is formed from a group of 4 employees in marketing and 7 employees in management. ​a) Find the probability that the committee has exactly 2 employees from marketing. ​b) Find the probability that the committee has at least one employee from marketing. ​c) Find the probability that the committee has at most one employee from management.

Answer 1

Answer: a) 0.25, b) 0.78, c) 0.71

Explanation:

Since we have given that

Number of employees in marketing = 4

Number of employees in management = 7

We need to hire committee of 3 people.

​a) Find the probability that the committee has exactly 2 employees from marketing.

So, Probability becomes

`(^4C_2* ^7C_1)/(^(11)C_3)\\\\=(42)/(165)\\\\=0.25`

​b) Find the probability that the committee has at least one employee from marketing.

`P(x\geq 1)=1-P(x=0)\\\\P(x\geq 1)=1-(^7C_3)/(^(11)C_3)=1-0.212=0.78`

c) Find the probability that the committee has at most one employee from management.

`P(x\leq 1)=P(x=0)+P(x=1)\\\\P(x\leq 1)=(^7C_3)/(^(11)C_3)+(^7C_2* ^4C_1)/(^(11)C_3)\\\\P(x\leq 1)=0.21+0.50=0.71`

Hence, a) 0.25, b) 0.78, c) 0.71