In each of following situations, state whether or not given assignment of probabilities to given outcomes is legitimate, that is, satisfies the rules of probability distribution. (The assignment of probabilities require not follow common sense understanding of outcomes!)
a. Roll a die and record 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. Select 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 card from shuffled deck: P(Clubs) = 12/52, P(Diamonds) = 12/52, P(Hearts) = 12/52, P(Spades) = 16/52.