Questions and Answers
What is the formula to calculate the probability of selecting 3 females and 2 males out of 11 finalists?
The probability can be calculated using the formula: P = (C(6,3) * C(5,2)) / C(11,5), where C(n,k) is the combination formula.
Calculate the probability of selecting 4 females and 1 male from the group of applicants.
The probability is P = (C(6,4) * C(5,1)) / C(11,5), which equals 0.227.
What is the probability of selecting all 5 females from the applicant pool?
The probability is P = C(6,5) / C(11,5), which equals 0.086.
Explain how to determine the probability of selecting at least 4 females.
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What does the term 'at least 4 females' imply in probability terms?
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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).
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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.
