Question

a. The probability that all 4 members on the committee will be girls is (Type an integer or a simplified fraction.)

Ask by Smith Clarke. in the United States
Jan 22,2025

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Answer

To find the probability that all 4 committee members are girls, you need to know the total number of members and how many of them are girls. The probability is calculated by dividing the number of ways to choose 4 girls by the total number of ways to choose any 4 members. Without specific numbers for girls and total members, I can't give a numerical answer.

Solution

To calculate the probability that all 4 members on the committee will be girls, we need to know the total number of members available and how many of them are girls. Let's denote: - \( G \): the number of girls - \( T \): the total number of members The probability \( P \) that all 4 members selected are girls can be calculated using the formula: \[ P = \frac{\text{Number of ways to choose 4 girls}}{\text{Total number of ways to choose 4 members}} \] The number of ways to choose 4 girls from \( G \) girls is given by the combination formula: \[ \binom{G}{4} = \frac{G!}{4!(G-4)!} \] The total number of ways to choose 4 members from \( T \) total members is: \[ \binom{T}{4} = \frac{T!}{4!(T-4)!} \] Thus, the probability can be expressed as: \[ P = \frac{\binom{G}{4}}{\binom{T}{4}} = \frac{\frac{G!}{4!(G-4)!}}{\frac{T!}{4!(T-4)!}} = \frac{G! \cdot (T-4)!}{T! \cdot (G-4)!} \] To provide a specific answer, I need the values of \( G \) and \( T \). Please provide those numbers.

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Mind Expander

If we're considering a committee made up of girls and boys, the probability of all members being girls depends on the total number of girls and boys available for selection. For example, if there are 6 girls and 4 boys, the total number of committee options would be \( \binom{10}{4} \), while the ways to choose 4 girls would be \( \binom{6}{4} \). To calculate the probability, you’d divide the combinations of choosing only girls by the total combinations available. Want to spice it up? Let’s say your middle school had a committee with 15 girls and 5 boys! The probability of selecting an all-girls committee would be the ratio of the ways to choose 4 girls to choosing any 4 members. With this scenario, it actually turns out to be a pretty sweet probability—just calculate \( \frac{\binom{15}{4}}{\binom{20}{4}} \) and you'll impress your friends with some math magic!

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