Each cell in the table represents a possible outcome of spinning the spinner twice. For example, the outcome of spinning A on the first spin and C on the second spin is represented by the cell in the second row and third column (A, C).
Part B:
To find how many times Martin should expect to spin C and then A in 400 trials, we need to determine the probability of spinning C on the first spin and A on the second spin.
From the table in part A, we can see that there are 16 possible outcomes, and that C is one of the four possible outcomes on the first spin. Therefore, the probability of spinning C on the first spin is 4/16 = 1/4.
Once C is spun on the first spin, there are three possible outcomes left for the second spin, and one of those outcomes is A. Therefore, the probability of spinning A on the second spin, given that C was spun on the first spin, is 1/3.
To find the probability of spinning C and then A, we multiply the probabilities of spinning C on the first spin and A on the second spin. That is:
P(C and A) = P(C) x P(A given C)
= (1/4) x (1/3)
= 1/12
Therefore, the expected number of times Martin should spin C and then A in 400 trials is:
Expected number of times = P(C and A) x number of trials
= (1/12) x 400
= 33.33
Therefore, Martin should expect to spin C and then A about 33 times in 400 trials.