Final answer:
The probability distribution represents the likelihood of each possible value of a random variable. In this case, the random variable X represents the number of times red is spun. The graph that represents this probability distribution would have the values 0, 9/33, and 24/33 plotted for X=0, X=1, and X=2.
Step-by-step explanation:
The probability distribution represents the likelihood of each possible value of a random variable. In this case, the random variable X represents the number of times red is spun. The sample space S consists of nine outcomes with one red spin and twenty-four outcomes with two red spins.
To find the probability distribution, we calculate the probability of each possible value of X. The probability of X=0 (no red spins) is 0, the probability of X=1 (one red spin) is 9/33, and the probability of X=2 (two red spins) is 24/33.
The graph that represents this probability distribution would have the values 0, 9/33, and 24/33 plotted on the y-axis for the corresponding values of X=0, X=1, and X=2 on the x-axis.