Probability Quiz: Gender Selection in Hiring

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).