Probability Quiz: Gender Selection in Hiring

Study Notes

Probability Calculations for Selecting Applicants

The total number of applicants consists of 6 females and 5 males, making a total of 11 finalists.
Positions to be filled: 5
Selection process is random.

Probability of Selecting 3 Females and 2 Males

To find the probability of selecting 3 females and 2 males, use the combination formula.
Calculate combinations:
- Choose 3 females from 6: C(6,3)
- Choose 2 males from 5: C(5,2)
Combine to find total favorable outcomes: C(6,3) * C(5,2).
Total ways to choose any 5 from 11: C(11,5).
Probability formula: P(3 females, 2 males) = (C(6,3) * C(5,2)) / C(11,5).

Probability of Selecting 4 Females and 1 Male

Use combinations to determine probability:
- Choose 4 females from 6: C(6,4).
- Choose 1 male from 5: C(5,1).
Total favorable outcomes: C(6,4) * C(5,1).
Probability formula: P(4 females, 1 male) = (C(6,4) * C(5,1)) / C(11,5).

Probability of Selecting 5 Females

Check feasibility: Only 6 females available, can select 5.
Calculate combinations:
- Choose 5 females from 6: C(6,5).
Total favorable outcomes: C(6,5) is the only combination.
Probability formula: P(5 females) = (C(6,5)) / C(11,5).

Probability of Selecting At Least 4 Females

This includes scenarios of selecting 4 females and 1 male, or 5 females.
Use previously calculated probabilities:
- Probability of selecting 4 females: P(4 females, 1 male)
- Probability of selecting 5 females: P(5 females)
Combine probabilities: P(at least 4 females) = P(4 females, 1 male) + P(5 females).

Description

This quiz explores the probability of selecting female and male applicants for 5 positions from a pool of 11 finalists. The questions focus on calculating probabilities for specific gender ratios, enhancing your understanding of combinatorics in probability. Test your skills with scenarios involving 3 females and 2 males, 4 females and 1 male, and more.