8. Sociology: Dating couples Do Couples get engaged or not? If they are engaged, how long did they date before becoming engaged? A poll of 1000 couples gave the following information:

Length of dating time before engagement

(a) Use the data to estimate the probability of each event for a dating couple chosen at random: The couple is not engaged, dated less than 1 year before getting engaged, dated 1 to 2 years before getting engaged, or dated more than 2 years.

Solution: We compute

(b) Do the probabilities of part (a) add up to 1? Why should they? What is the sample space in this problem?

Solution: They do, and they should because they form a partition of the sample space, which means they’re disjoint events that account for all the cases.