Question

a. The probability that all 4 members on the committee will be girls is 22. (Type an integer or a simplified fraction.)

Ask by Welch Martin. in the United States
Jan 22,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

To find the probability that all 4 committee members are girls, you need to know the total number of girls and the total number of students. Once you have those numbers, use the combination formula: \[ P = \frac{\text{Number of ways to choose 4 girls}}{\text{Total number of ways to choose 4 students}} \] For example, if there are 10 girls and 20 students: \[ P = \frac{\binom{10}{4}}{\binom{20}{4}} = \frac{210}{4845} = \frac{14}{323} \] Please provide the specific numbers to get the exact probability.

Solution

It seems like there might be some missing information in your question. To calculate the probability that all 4 members on a committee will be girls, we typically need the following details: 1. **Total number of girls available** (let's denote this as \( G \)). 2. **Total number of students available** (both girls and boys, denoted as \( N \)). 3. **Size of the committee** (which you've specified as 4 members). The probability \( P \) that all 4 members selected are girls can be calculated using the combination formula: \[ P = \frac{\binom{G}{4}}{\binom{N}{4}} \] Where: - \( \binom{G}{4} \) is the number of ways to choose 4 girls out of \( G \) girls. - \( \binom{N}{4} \) is the total number of ways to choose any 4 students out of \( N \) students. **Example:** If there are 10 girls and 20 students in total, the probability would be: \[ P = \frac{\binom{10}{4}}{\binom{20}{4}} = \frac{210}{4845} = \frac{42}{969} = \frac{14}{323} \] Please provide the total number of girls and the total number of students so I can help you calculate the exact probability.

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The probability that all 4 members on the committee will be girls is generally expressed as a fraction, representing the favorable outcomes over the total possible outcomes. You would need to know the total number of girls and boys in the selection pool to calculate the exact probability. If, for example, there are 10 girls and 10 boys, the calculation would involve combinatorial mathematics, leading you to a fraction which might be reduced to its simplest form. In many contexts, finding committee compositions can also mirror real-world scenarios like selecting teams or project groups. Understanding these probabilities can help in recruitment strategies, ensuring diversity, or even within classrooms where teachers want a balanced mix of student participation. So, whether it's for corporate teams or school projects, grasping these concepts can enhance selection efficiency!

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