From a group of 10 boys and 13 girls, a committee of 5 students is chosen at random. a. What is the probability that all 5 members on the committee will be girls? b. What is the probability that all 5 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 5 members on the committee will be girls is \( \frac{117}{3059} \). (Type an integer or a simplified fraction.) b. The probability that all 5 members on the committee will be boys is \( \frac{36}{4807} \). (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.)

To determine the probability that there will be **at least one girl** on the committee, we can use the complementary probability approach. This involves calculating the probability of the opposite event (i.e., **all committee members are boys**) and then subtracting that from 1. ### Step-by-Step Solution: 1. **Total Number of Students:** - Boys: 10 - Girls: 13 - **Total:** \( 10 + 13 = 23 \) students 2. **Total Number of Ways to Choose 5 Students:** \[ \binom{23}{5} = \frac{23!}{5!(23-5)!} = 33,649 \] 3. **Number of Ways to Choose 5 Boys:** \[ \binom{10}{5} = \frac{10!}{5!(10-5)!} = 252 \] - **Probability that all 5 members are boys:** \[ P(\text{all boys}) = \frac{252}{33,649} = \frac{36}{4,807} \] 4. **Probability of At Least One Girl:** \[ P(\text{at least one girl}) = 1 - P(\text{all boys}) = 1 - \frac{36}{4,807} = \frac{4,807 - 36}{4,807} = \frac{4,771}{4,807} \] - This fraction is already in its simplest form since 4,771 and 4,807 are coprime (their greatest common divisor is 1). ### Final Answer: c. The probability that there will be at least 1 girl on the committee is \( \frac{4771}{4807} \). **Answer:** Problem c Answer: The probability is \( \frac{4771}{4807} \).