Question

video lesson 5.2 example 4 - finding the probability of dependent events

1. nine women and six men are on a committee. two people are randomly chosen from the committee members to serve as a chairperson and a treasurer. find the probability that both events a and b will occur.

a: the chairperson is a man.
b: the treasurer is a woman.

Explanation:

Step1: Find total committee members

Total members = 9 women + 6 men = 15.

Step2: Probability of Event A (chairperson is man)

Number of men = 6, so \( P(A) = \frac{6}{15} = \frac{2}{5} \).

Step3: Probability of Event B after A (treasurer is woman)

After choosing a man as chairperson, remaining members = 14, women = 9. So \( P(B|A) = \frac{9}{14} \).

Step4: Probability of A and B (dependent events)

Use formula \( P(A \cap B) = P(A) \times P(B|A) \).
Substitute values: \( \frac{2}{5} \times \frac{9}{14} = \frac{18}{70} = \frac{9}{35} \).

Answer:

\(\frac{9}{35}\)