31. In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate—that is, satisfies the rules of probability. If not, give specific reasons for your answer.
31.
(a) Not legitimate: The probabilities are between 0 and 1, but the sum is greater than 1. Rule 2 is violated.
(b) Legitimate: The probabilities are between 0 and 1, inclusively, and have sum 1.
One may find it surprising that no student surveyed was born in fall, but that outcome is possible.