Veronique has a spinner with three sections of equal size, red (r), green (g), and blue (b).The spinner is spun twice. The sample space for the possible outcomes is S = {rr, rb, rg, gr, gg, gb, br, bg, bb}. If the number of times red is spun is the random variable, X, which graph represents the probability distribution?

The color red can only appear 0,1 or 2 times. We also have that there are in total 9 outcomes. Hence, each event has the same probability, 1/9. Since the definition of probability is the number of favorable outcomes over the total number of outcomes, we get that since in 1 outcome we have both spins turning red, the probability of 2 times appearing red is 1/9. We also have 4 spins where there is only one red; rb, rg, gr, br. Hence, the probability is 4/9. Now, we have 4 outcomes where there is no red. Hence, the probability for 0 reds is also 4/9.
Succinctly P(0 reds)=4/9, P(1 red)=4/9, P(2 reds)= 1/9