We are asked to calculate the probabilities related to selecting a committee of 5 students from a group of 11 boys and 13 girls.

Total number of students:

$11 \text{ boys} + 13 \text{ girls} = 24 \text{ students}$

Total possible ways to form a committee of 5 students from 24:

The number of ways to choose 5 students from 24 is calculated using combinations: $\binom{24}{5} = \frac{24!}{5!(24-5)!} = \frac{24!}{5!19!}$

Now let's go step-by-step through each part of the question.

Part 1 (a): Probability that all 5 members on the committee are girls

The number of ways to choose 5 girls from the 13 available girls: $\binom{13}{5} = \frac{13!}{5!(13-5)!} = \frac{13!}{5!8!}$

The probability that all 5 members are girls is: $\text{Probability} = \frac{\binom{13}{5}}{\binom{24}{5}}$

Part 2 (b): Probability that all 5 members on the committee are boys

The number of ways to choose 5 boys from the 11 available boys: $\binom{11}{5} = \frac{11!}{5!(11-5)!} = \frac{11!}{5!6!}$

The probability that all 5 members are boys is: $\text{Probability} = \frac{\binom{11}{5}}{\binom{24}{5}}$

Part 3 (c): Probability that there will be at least 1 girl on the committee

The complement of this event is that there are no girls, meaning all 5 members are boys. We already computed the probability that all 5 members are boys in part (b), so the probability of at least 1 girl is: $\text{Probability} = 1 - \text{(Probability that all 5 members are boys)}$

Let me calculate these values.### Part 1 (a): The probability that all 5 members of the committee will be girls is approximately: $0.0303$

Part 2 (b):

The probability that all 5 members of the committee will be boys is approximately: $0.0109$

Part 3 (c):

The probability that there will be at least 1 girl on the committee is approximately: $0.9891$

Would you like more details on how these probabilities were calculated or have any specific questions?

Here are 5 related questions to deepen your understanding:

1. What is the probability of forming a committee with exactly 3 girls and 2 boys?
2. How does the probability change if the group has more boys than girls?
3. Can you explain how the complement rule helps in calculating the probability of at least 1 girl?
4. How would the probabilities change if the committee had 6 members instead of 5?
5. What is the probability of selecting a committee with at least 2 boys?

Tip: Always double-check if the question asks for a simplified fraction or a decimal approximation when solving probability problems.