You were on the right track. Here are two ways to go about it.
• By definition of conditional probability,
Pr[A | B] = Pr[A and B] / Pr[B]
Out of the total 100 participants in the survey, there are 18 people that both have a positive attitude and are over 35, so
Pr[positive and over 35] = 18/100
Out of the 100 pariticipants, 40 are over 35, so
Pr[over 35] = 40/100
Then the conditional probability you want is (18/100) / (40/100) = 18/40 = 9/20.
• There are 40 people over 35 in the survey. You want the probability that someone randomly chosen from this group has a positive attitude, of which there are 18. Hence the probability is 18/40 = 9/20.
