Question

It is estimated that, of the people viewing a certain movie over the weekend, 45 percent were adult women, 42 percent were adult men, and 13 percent were children.

If we randomly interview people at a theatre about the movie, each interview takes a few minutes, so we will not interview people in the same group or family. So we may assume that their gender and age classification is independent from person to person.

a. What is the probability that the first five people we interview are all adults?

b. What is the probability that the first adult we interview is a female?

Answer 1

O the people viewing a certain movie

probabality a randomly chosen person is an adult women = P(W) = 45% = 0.45

probabality a randomly chosen person is an adult man = P(M) = 42% = 0.42

Probablity the chosen person is adult = P(A)= 0.45 + 0.42 = 0.87

Probablity the chosen person is children = P(C) = 0.13

a.

The probability that the first five people we interview are all adult

= P(A) * P(A)* P(A)* P(A)* P(A)

= (0.87)⁵

= 0.498

b.

The probability that the first adult we interview is a female

or simple words

Probabality of choosing a woman given that we are to select the female amonsgt adults

P( W | A ) = P( W A ) / P(A)

= P(W) / P(A)

= 0.45 / 0.87

= 0.517