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Theoretical
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Theoretical
Experimental
and
Probability
Key Vocabulary
Experiment= An investigation or procedure that has varying results.
Outcomes= The possible results of an experiment.
Event= A collection of one or more outcomes.
Favorable Outcomes= the outcomes of a specific event.
What is Experimental Probability?
Probability that is based on the repeated trials of an experiment is called Experimental Probability. In order to find the experimental probability of an experiment, you must divide the number of times the event occurs by the total number of trials.
What is Theoretical Probability?
Probability that is the comparison of the number of favorable outcomes to the number of possible outcomes when all possible outcomes are all equally likely is called Theoretical Probability. This type of probability supposedly how likely it is for your event to occur.
Example Question #1:
The bar graph shows the results of spinning a spinner 200 times. Find the Experimental Probability of spinning a 4.
Claim:
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Evidence:
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Reasoning:
In order to find experimental probability, you must divide the number of times the event occurs by the total number of trials. There were 37 times that a 4 was spun, according to the graph, and a total of 200 spins were performed. Then, to find the percent, you must divide the numerator of the fraction (37) by its denominator (200), as shown. So, according to the experimental probability, you have an 18.5% chance of spinning a 4.
Example Question #2:
The table to the left shows the results of flipping the same two coins 100 times each. Find the experimental probability of flipping a head twice.
H=heads T=tails
Claim:
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Evidence:
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Reasoning:
In order to find experimental probability, you must divide the total number of times the event occurs by the total number of trials. In this experiment, two heads were flipped 23 times, and the two coins were flipped 100 times. Then in order to find the percent, you must divide 23 (numerator) by 100 (denominator) to get the percent. So according to this experiment, you have a 23% chance of flipping heads twice.
Example Question #3:
Find the Theoretical Probability of spinning an even number.
Claim:
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Evidence:
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Reasoning:
According to the formula, you must divide the number of favorable outcomes by the number of possible outcomes to find the theoretical probability. Then, as before, you must divide the numerator by the denominator in order to find the percentage. The theoretical probability of this event states that, in theory, you have a 50% chance of spinning an even number.
What is Probability?
Probability of an event is a number that measures the likeliness of an event to occur. Probabilities are measured between 0, which is impossible, to 1, which is certain.
Example Question #4:
You have these letter tiles in a bag. What is the theoretical probability of picking out not an R?
Claim:
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Evidence:
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Reasoning:
This evidence proves that my claim is correct, because based on the formula that you must use in order to find theoretical probability, you must divide the number of favorable outcomes (6) by the number of possible outcomes (7). Then, when you divide the numerator by the denominator, to find the percentage, you get 85.7%. This theoretical probability states that theoretically, you have an 85.7% of not picking out an R.