Question: In each of the following situations, state whether or not the given assignment of probabilities to given outcomes is legitimate, that is, satisfies the rules of a probability distribution. (The assignment of probabilities need not follow common sense understanding of the outcomes!)

a. Roll a die and record the count of spots on the up face: P(1) = 0, P(2) = 1/6, P(3) = 1/3, P(4) = 1/3, P(5) = 1/6, P(6) = 0.

b. Choose a college student at random and record sex and enrollment status: P(female-fulltime) = 0.56, P(female-part time) = 0.24, P(male-fulltime) = 0.44, P(male- part time) = 0.17

c. Deal a card from a shuffled deck: P(Clubs) = 12/52, P(Diamonds) = 12/52, P(Hearts) = 12/52, P(Spades) = 16/52.