Respuesta :
Answer:
Probability = 0.6
Step-by-step explanation:
We are given that out of 6 employees, 3 have been with the company for five or more years which means remaining 3 employees have been with the company for less than 5 years.
We have to find the probability that If 4 employees are chosen randomly from the group of 6, what is the probability that exactly 2 will have five or more years seniority;
This means that 2 employees will be selected from the group of 3 employees who are with the company for five or more years and remaining 2 employees will be selected from the group of 3 employees who have been with the company for less than 5 years.
Number of ways in which exactly 2 will have five or more years seniority
= [tex]^{3} C_2 * ^{3} C_2[/tex]
Total number of ways for selecting 4 employees from group of 6 = [tex]^{6} C_4[/tex]
So, required probability = [tex]\frac{^{3} C_2*^{3} C_2}{^{6} C_4}[/tex] = [tex]\frac{3!}{2!*1!}* \frac{3!}{2!*1!} * \frac{4!*2!}{6!}[/tex] {[tex]\because ^{n}C_r = \frac{n!}{r!*(n-r)!}[/tex] }
= [tex]\frac{3*2!}{2!}*\frac{3*2!}{2!}*\frac{4!*2!}{6*5*4!}[/tex] = [tex]\frac{18}{30}[/tex] = 0.6
