Question

A pollster plans to call adults. She has a list of names and numbers of 100 adults, consisting of 60 males and 40 females. She will make random selections and will not call the same person more than once.

a. Consider the event of getting a male on the first selection and getting a female on the second selection. Are these independent or dependent events?

b. What is the probability of getting a male on the first selection and getting a female on the second selection?

Answer 1

Part (a)

Let A represent the event the first selection is a male and B represent the event the second selection is a female.

 

Then, P(B/A) = 40/99 and P(B/AC) = 39/99.

 

Thus, probability of B depends on whether A has occurred or not. Hence,

 

These two events are DEPENDENT.

 

 If the selection were with replacement, meaning that the same person could be called again, the two events will be independent.

 

Part (b)

For the first selection there are 60 possibilities and for the second 40 possibilities. Thus, totally there are 2400 possibilities.

 

Now, without any restriction, there are 100 ways for the first selection and 99 for the second selection implying that there are 9900 possibilities in total.

 

Hence, the required probability = 2400/9900 = 8/33.

a. These two events are DEPENDENT.

b. Hence, the required probability = 2400/9900 = 8/33.