Question

1. At a large block party, there are 50 men and 40 women. You want to ask opinions about how to improve the next party. You choose at random five of the men and separately choose at random four of the women to interview.

(a) What is the probability that any of the 50 men is in your random sample of five men to be interviewed? What is the probability that any of the 40 women is in your random sample of four women to be interviewed?

(b) If you have done the calculations correctly in part (a), the probability of any person at the party being interviewed is the same. Why is your sample of nine men and women not an SRS of people from the party?

Answer 1

a) Probability of drawing a particular man in the 5 men selected out of the 50 men is computed here as:

Similarly now the probability of drawing a particular woman in the 4 women selected out of the 40 women is computed here as:

Therefore 0.1 is the required probability here too.

b) The drawing of a random sample in this case is not a case of a simple random sampling but a case of a stratified random sampling . This is because we are not drawing the 9 people randomly from 90 people but we are making sure that we are drawing 5 men from a subgroup of 50 men and then 4 women from the subgroup of 40 women.