The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 20 trials Outcome Number of Trials 0 0 1 3 2 1 3 1 4 4 5 2 Answer the following. Round your answers to the nearest thousandths. 6 (4 T 1 8 3 (a) From these results, compute the experimental probability of getting a S. 0 (b) Assuming that the machine is fair, compute the theoretical probability of getting a 8. 1 (c) Assuming that the machine is fair, choose the statement below that is true. The experimental and theoretical probabilities must always be equal. 9 1 As the number of trials increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. O As the number of trials increases, we expect the experimental and theoretical probabilities to become farther apart.
The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 20 trials Outcome Number of Trials 0 0 1 3 2 1 3 1 4 4 5 2 Answer the following. Round your answers to the nearest thousandths. 6 (4 T 1 8 3 (a) From these results, compute the experimental probability of getting a S. 0 (b) Assuming that the machine is fair, compute the theoretical probability of getting a 8. 1 (c) Assuming that the machine is fair, choose the statement below that is true. The experimental and theoretical probabilities must always be equal. 9 1 As the number of trials increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. O As the number of trials increases, we expect the experimental and theoretical probabilities to become farther apart.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:This image shows a table and questions related to a probability experiment conducted by a state lottery board. The board tested a machine that randomly selects lottery numbers, with each trial producing a ball marked with one of the digits 0 through 9. The machine was tested for 20 trials, and the results are displayed in the table below:
### Table: Number of Trials vs. Outcome
| Outcome | Number of Trials |
|----------|------------------|
| 0 | 1 |
| 1 | 1 |
| 2 | 3 |
| 3 | 4 |
| 4 | 2 |
| 5 | 1 |
| 6 | 1 |
| 7 | 1 |
| 8 | 3 |
| 9 | 3 |
### Questions:
1. **(a)** From these results, compute the experimental probability of getting an 8.
2. **(b)** Assuming that the machine is fair, compute the theoretical probability of getting an 8.
3. **(c)** Assuming that the machine is fair, choose the statement below that is true:
- As the number of trials increases, we expect the experimental and theoretical probabilities to become closer or equal.
- The experimental and theoretical probabilities will always be equal.
- As the number of trials increases, we expect the experimental and theoretical probabilities to become further apart.
This exercise involves calculating the probability based on experimental data and comparing it with theoretical probability, assuming a fair machine.
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