Legitimate probabilities? 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.

(a) When a coin is spun, P(H) = 0.55 and P(T) = 0.45.

(b) When two coins are tossed, P(HH) = 0.4, P(HT) = 0.4, P(TH) = 0.4, and P(TT) = 0.4.

(c) Plain M&M’s have not always had the mixture of colors given in Exercise 18.13. In the past there were no red candies and no blue candies. Tan had probability 0.10 and the other four colors had the same probabilities that are given in Exercise 18.13.