When would you expect the experimental probability of an event to be closest to its theoretical probability?
When the results of 10 trials were used in calculating the theoretical probability
When the results of 10 trials were used in calculating the experimental probability
When the results of 100 trials were used in calculating the experimental probability
None of the above, because the experimental probability is unrelated to the theoretical probability.
Now really, which do you think?
The theoretical probability of heads in a coin toss is .5
If you toss it 100 times are you not more likely to get closer to .5 on the average than if you toss it ten times?
How likely are you to toss ten heads in a row?
How likely are you to toss 100 heads in a row ? :)
I guess 10 trials theoretically
10
To determine when the experimental probability of an event would be closest to its theoretical probability, we need to understand the difference between these two concepts.
Theoretical probability is based on mathematical calculations and assumes that all possible outcomes are equally likely. For example, the theoretical probability of rolling a 6 on a standard six-sided die is 1/6 because there is only one outcome that satisfies the condition out of six possible outcomes.
On the other hand, experimental probability is based on actual observations or trials. It involves conducting an experiment or series of trials to determine the likelihood of a particular outcome. The experimental probability can be close to the theoretical probability if enough trials or observations are conducted.
Given the options provided, it is most likely that the experimental probability would be closest to the theoretical probability when the results of 100 trials were used in calculating the experimental probability. The more trials conducted, the more accurate the experimental probability will be in reflecting the theoretical probability. The Law of Large Numbers states that as the number of trials increases, the experimental probability approaches the theoretical probability.
Therefore, out of the options given, using the results of 100 trials in calculating the experimental probability is more likely to yield results that are closer to the theoretical probability.