To find the expected value of the random variable X, which is the maximum of the two numbers on the spinners, we need to consider all possible outcomes of the two spinners and calculate their probabilities.
There are nine possible outcomes for the two spinners: (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), and (3, 3). The probability of each outcome is 1/9, since there are three possible outcomes for each spinner and each outcome is equally likely.
For each possible outcome, we can calculate the value of X, which is the maximum of the two numbers on the spinners. For example, if the outcome is (1, 2), then X = 2. If the outcome is (3, 3), then X = 3.
We can then multiply the value of X for each outcome by its probability, and sum the results to find the expected value of X.
For example, the expected value of X for the outcome (1, 1) is 1 * (1/9) = 1/9. The expected value of X for the outcome (1, 2) is 2 * (1/9) = 2/9. The expected value of X for the outcome (1, 3) is 3 * (1/9) = 3/9. And so on.
We can do this for all nine outcomes to find the expected value of X. The expected value of X is the sum of all the expected values of X for each outcome, which is:
E[X] = (1/9) + (2/9) + (3/9) + (2/9) + (3/9) + (3/9) + (3/9) + (3/9) + (3/9) = 20/9 = 2.222...
So, the expected value of the random variable X, which is the maximum of the two numbers on the spinners, is approximately 2.222.