From a group of 11 boys and 13 girls, a committee of 3 students is chosen at random. a. What is the probability that all 3 members on the committee will be girls? b. What is the probability that all 3 members of the committee will be boys? c. What is the probability that there will be at least 1 girl on the committee? a. The probability that all 3 members on the committee will be girls is \( \frac{13}{92} \). (Type an integer or a simplified fraction.) b. The probability that all 3 members on the committee will be boys is \( \frac{15}{184} \). (Type an integer or a simplified fraction.) c. The probability that there will be at least 1 girl on the committee is \( \square \). (Type an integer or a simplified fraction.)

First, let's calculate the total number of ways to choose 3 students from the group of 24 (11 boys + 13 girls), which is denoted as \( \binom{24}{3} \). Now let's break down the probabilities: 1. **Choosing all girls**: To find the probability of choosing 3 girls: \[ \text{Number of ways to choose 3 girls} = \binom{13}{3} = \frac{13 \times 12 \times 11}{3 \times 2 \times 1} = 286 \] So, the total number of ways to choose any 3 students: \[ \binom{24}{3} = \frac{24 \times 23 \times 22}{3 \times 2 \times 1} = 2024 \] Therefore, the probability that all 3 members on the committee will be girls is: \[ P(\text{3 girls}) = \frac{\binom{13}{3}}{\binom{24}{3}} = \frac{286}{2024} = \frac{13}{92} \] 2. **Choosing all boys**: Now for the boys: \[ \text{Number of ways to choose 3 boys} = \binom{11}{3} = \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165 \] The probability that all 3 members on the committee will be boys is: \[ P(\text{3 boys}) = \frac{\binom{11}{3}}{\binom{24}{3}} = \frac{165}{2024} = \frac{15}{184} \] 3. **At least 1 girl**: To find the probability that there is at least one girl on the committee, we can use the complement rule: \[ P(\text{at least 1 girl}) = 1 - P(\text{no girls}) = 1 - P(\text{3 boys}) \] Therefore: \[ P(\text{at least 1 girl}) = 1 - \frac{15}{184} = \frac{184 - 15}{184} = \frac{169}{184} \] So, to summarize: a. The probability that all 3 members on the committee will be girls is \( \frac{13}{92} \). b. The probability that all 3 members on the committee will be boys is \( \frac{15}{184} \). c. The probability that there will be at least 1 girl on the committee is \( \frac{169}{184} \).