The spinner below shows 5 equally sliced slices. Christine spun the dial 40 times and got the following results.

Outcome White Grey Black
Number of spins 12 16 12

Fill in the table below. Round your answers to the nearest thousandth.

(a) Assuming that the spinner is fair, compute the theoretical probability of landing on black.

(b) From Christine’s results, compute the experimental probability of landing on black.

(c) Assuming that the spinner is fair, choose the statement below that is true:
A. As the number of spins increases, we expect the experiment and probabilities to become closer though they might not be equal.
B. The experimental and theoretical probabilities mist always be equal.
C. As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.