Comparing Theoretical & Experimental Probability

Comparing Theoretical & Experimental Probability
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  • 0:03 Types of Probabilities
  • 2:05 Comparing Probabilities
  • 2:58 Consistency
  • 4:41 Cannot Compute
  • 5:25 Lesson Summary
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Lesson Transcript
Instructor: Catherine Glover

Catherine has a master's degree in Mathematical Biology and teaches math at the college level.

Did you know there's more than one kind of probability? Complete this lesson to compare theoretical probability with experimental probability. They're not the same!

Types of Probabilities

Sam has a bag of jelly beans with five different flavors: raspberry, strawberry, watermelon, lemon, and lime. The bag states that there are 50 jelly beans of each flavor, for a total of 250 jelly beans. Sam's very favorite flavor is lemon, and he hopes that's the first jelly bean he gets from the bag. What are the chances that he'll get a lemon jelly bean?

We can answer this question in two ways. The first way is to determine the theoretical probability, which is the change of an event occurring based on knowledge alone, of picking a lemon jelly bean out of the bag. You can calculate the theoretical probability by dividing the number of ways you can get a lemon jelly bean, by the total number of jelly beans. There are 50 lemon jelly beans out of 250 total jelly beans, which means the theoretical probability of getting a lemon jelly bean is 50/250 = 0.2, or 20% when expressed as a percentage.

The second way to answer this question is more fun - by actually doing an experiment! In this case, selecting a jelly bean from the bag is the experiment. If we actually choose some jelly beans out of a bag like the one we've described, we can record the flavors of jelly beans we actually get. In this way, we can determine the experimental probability, which is the change of an event occurring based on experiments actually performed or data actually collected, of getting a lemon jelly bean by dividing the number of times we actually got a lemon jelly bean by the total number of jelly beans we picked out of the bag. For example, if we got 6 lemon jelly beans out of a total of 20 jelly beans selected from the bag, then the experimental probability of getting a lemon jelly bean would be 6/20 = 0.3, or 30% when expressed as a percentage.

Comparing Probabilities

So what's the big difference between theoretical and experimental probabilities? The main difference is that a theoretical probability is calculated based only on the knowledge of the situation. If you know how many different ways an event can occur and you know the total number of events that can occur, then you can calculate the theoretical probability of the event occurring. All you need is knowledge!

In comparison, you need to actually perform an experiment, test, or trial, or already have data from such experiments, to calculate an experimental probability. This is because you need to know the number of times an event did occur, and the number of times you performed the experiment, in order to perform the calculation.

As we have seen, the theoretical and experimental probabilities were not the same. That doesn't mean we did anything wrong, we just answered the question in two slightly different ways.

Consistency

Another difference is in regard to the consistency of your probability. Theoretical probabilities are constant, as long as the conditions don't change. If Sam has 30 bags of jelly beans exactly like the one described earlier, then the theoretical probability of choosing a lemon jelly bean from any bag will always be 20%. This is because the conditions are the same in every bag: 50 lemon jelly beans out of a total of 250.

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