An example of theoretical probability from the considered option is given by: Option 2: A spinner has 8 equal sections numbered 1 to 10. The probability of spinning the number 3 is 1/8
Experimental probability calculates the probability of some event from the results of experiments.
For an event E, we get the experimental probability of that event
[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]
where, [tex]P_e(E)[/tex]is denoting experimental probability of occurrence of E.
Probability which is derived theoretically, irrespective of what outcome comes, is called theoretical probability. Probabiltiy which is based on the outcomes of experiments performed is called experimental probability.
Suppose we want to find the probability of an event E.
Then, its theoretical probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
Checking all the options to see which one gives theoretical probability:
This option uses what was observed from one result. Thus, 3/5 is experimental probability here, as there is no evidence of it being theoretical probability but enough support towards being experimental probability.
No experiment is done here, just the description of the setup of the random experiment.
Now, E = event of getting 3 on the spinner.
All spinner's parts are assumingly equally likely, we have:
Number of ways E can occur = 1
Number of ways spinner's outcome can come = 8
Thus, we get P(E) = 1/3
Thus, this option is demonstrating theoretical probability.
This is using experimental results to get the estimated probability.
Actually, assuming coin being fair, both the tail and heads being equally probable, if we take:
E = event of getting head, then as there are two results possible being Tail or Head (assuming only 2 results), and there is one way of getting head in one toss, so we get:
P(E) = 1/2 = 0.5
Thus, this option is demonstrating experimental probability instead of theoretical one.
It is using the data from one experiment. So its experimental probability. Sometimes we can get experimental probability = theoretical probability value, but still, there'd be difference of how you calculated it from the start. Usually, if calculated from experiment, then its experimental probability, and if calculated virtually and based on theories, it is theoretical probability.
Thus, an example of theoretical probability from the considered option is given by: Option 2: A spinner has 8 equal sections numbered 1 to 10. The probability of spinning the number 3 is 1/8
Learn more about experimental probability here:
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