Question

A company consists of 15 employees of which 5 are women If 11 employees are chosen at random to form a team and work on a project, then what is the chance of obtaining at least 3 women in the team? 12/13 7/13 6/13 11/15 ​

Answer 1

the probability of this is 11/15

Answer 2

Given:

A company has 15 employees with 5 women among them. 11 are chosen at random among them with at least 3 women.

To Find:

The probability of selecting a team of 11 members with at least 3 women.

Solution:

The given question can be solved by using the concepts of probability and permutations and Combinations.

1. It is given that the team is of 15 members out of which 5 are women and 10 are men.

2. Selection of 11 members from the team of 15 in which at least 3 women are included is given by,

=> 11 members team with 3 women + 11 members team with 4 women + 11 members team with 5 women.

3. Probability(at least 3 women out of 11) = (Favorable outcomes)/ (Total number of outcomes)

=> Selection of 11 members with 3 women = $5C_{3} * 10C_{8}$ possibilities,

=> Selection of 11 members with 4 women = $5C_{4}*10C_{7}$ possibilities,

=> Selection of 11 members with 5 women = $5C_{5}*10C_{6}$ possibilities,

=> Total possibilities for forming a team of 11 members =$15C_{11}$.

Probability for forming a team of 11 members with at least 3 women =

=>$\frac{5C_{3}*10C_{8} + 5C_{4}*10C_{7}+5C_{5}*10C_{6} }{15C_{11} }$,

=> (450+600+210/1365),

=> (1260/1365) ( Factorize into simplest terms),

=>  (12/13).

Therefore, the probability of selecting a team of 11 members from 15 members with at least 3 out 5 women is 12/13.