In a game, a fair 4-sided spinner with edges labelled 0, 1, 2 and 3 is spun. If a player spins 1, 2 or 3, then that is their score. If a player scores 0, then they spin a fair triangular spinner with edges labelled 0,1 and 2, and the number they spin is their score. Let the variable X represent a player’s score.

a Show that P(X = 0) = 1/12.

b. Draw up the probability distribution table for X, and find the probability that X is a prime number.