To fill in the table and compute the probabilities, we first need to clarify the specific digit the lottery board is focusing on (for the underlined part in your question). I'll assume it's the digit '0' for the sake of this exercise.
Here's how we will compute theoretical and experimental probabilities:
(a) Theoretical Probability
If the machine is fair and you are dealing with digits 0-9, there are a total of 10 possible outcomes (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). The theoretical probability of picking any specific digit (like '0') is calculated as:
\[ P(\text{getting a '0'}) = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{1}{10} = 0.1 \]
Rounded to the nearest thousandth, this would be:
\[ P(\text{getting a '0'}) = 0.100 \]
(b) Experimental Probability
To compute the experimental probability, we need the number of times the digit '0' was picked during the trials. Assuming you have your results from the trials as follows (you will need to fill this based on your data):
- Let's say out of 100 trials, the digit '0' was picked 12 times.
The experimental probability would then be calculated as:
\[ P(\text{getting a '0'}) = \frac{\text{Number of times '0' is picked}}{\text{Total number of trials}} = \frac{12}{100} = 0.12 \]
Rounded to the nearest thousandth, this would be:
\[ P(\text{getting a '0'}) = 0.120 \]
(c) True Statement
The correct statement regarding the difference between experimental and theoretical probabilities, given a large number of trials, is:
"With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small."
This statement reflects that while experimental and theoretical probabilities can differ, they tend to converge as the number of trials increases, due to the Law of Large Numbers.
If you have specific numbers from your trials, please share them, and I can help you calculate the experimental probability accordingly!
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