a. What is the probability that all 4 members on the committee will be girls? b. What is the probability that all 4 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 4 members on the committee will be girls is \( \frac{9}{133} \). (Type an integer or a simplified fraction.) b. The probability that all 4 members on the committee will be boys is \( \frac{\frac{42}{1463}}{\text {. }} \). (Type an integer or a simplified fraction.)

To solve the problem, we need to analyze the probabilities based on the information provided. Let's denote: - \( G \): the number of girls - \( B \): the number of boys - \( N \): the total number of committee members From the information given, we have: 1. The probability that all 4 members on the committee will be girls is \( P(G) = \frac{9}{133} \). 2. The probability that all 4 members on the committee will be boys is \( P(B) = \frac{42}{1463} \). ### a. Probability that all 4 members will be girls This is already provided as: \[ P(G) = \frac{9}{133} \] ### b. Probability that all 4 members will be boys This is provided as: \[ P(B) = \frac{42}{1463} \] ### c. Probability that there will be at least 1 girl on the committee To find the probability that there is at least 1 girl on the committee, we can use the complement rule. The complement of having at least 1 girl is having no girls at all (i.e., all boys). Therefore, we can express this as: \[ P(\text{at least 1 girl}) = 1 - P(\text{all boys}) \] Substituting the value of \( P(B) \): \[ P(\text{at least 1 girl}) = 1 - \frac{42}{1463} \] Now, we need to calculate this probability. Let's perform the calculation for \( P(\text{at least 1 girl}) \): \[ P(\text{at least 1 girl}) = 1 - \frac{42}{1463} = \frac{1463 - 42}{1463} = \frac{1421}{1463} \] ### Summary of Results a. The probability that all 4 members on the committee will be girls is \( \frac{9}{133} \). b. The probability that all 4 members on the committee will be boys is \( \frac{42}{1463} \). c. The probability that there will be at least 1 girl on the committee is \( \frac{1421}{1463} \).