The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 40 trials and got the following results.
0 1 2 3 4 5 6 7 8 9
Number of Trials 7 3 5 2 7 3 2 1 46
Fill in the table below. Round your answers to the nearest thousandth.
Outcome
(a) Assuming that the machine is fair, compute the theoretical probability of getting a 0.
(b) From these results, compute the experimental probability of getting a 0.
0
(C) Assuming that the machine is fair, choose the statement below that is true:
The experimental and theoretical probabilities must always be equal.
As the number of trials increases, we expect the experimental and theoretical
probabilities to become closer, though they might not be equal.
As the number of trials increases, we expect the experimental and theoretical
probabilities to become farther apart.