What is Theoretical Probability?

The study of probcapacity deserve to be split into two areas:

Theoretical Probability is the theory behind probcapacity.

You are watching: Which of the following is an example of theoretical probability

Experipsychological (empirical) probability is probcapability calculated throughout experiments, straight monitoring, endure, or practice.

With theoretical probability, you don’t actually conduct an experiment (i.e. roll a die or conduct a survey). Instead, you use your understanding around a instance, some logical reasoning, and/or known formula to calculate the probcapacity of an event happening. It deserve to be written as the proportion of the number of favorable occasions divided by the variety of possible occasions. For example, if you have actually 2 raffle tickets and also 100 tickets were sold:

Number of favorable outcomes: 2Number of feasible outcomes: 100Ratio = variety of favorable outcomes / variety of possible outcomes = 2/100 = .5.

A theoretical probcapacity distribution is a known distribution choose the normal circulation, gamma distribution, or one of dozens of other theoretical distributions.


Theoretical Probability Example

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Example question: What is the theoretical probcapability of rolling a 4 or a 7 through a collection of two dice?If this question asked you the empirical probability, you can erected an experiment. For example, you can roll the die a hundred times, document the results and also state the probcapability. But as this question is asking you the theoretical probcapacity, you have to use a formula or erected a sample room. As tright here is no single formula for calculating die rolling probabilities, erected a sample space.Step 1: Set up a sample room. In various other words, create out all of the feasible “events” that deserve to take place. In this situation, the occasions are the numbers that come up after the dice are rolled. For two dice, the probabilities are:<1><1>, <1><2>, <1><3>, <1><4>, <1><5>, <1><6>,<2><1>, <2><2>, <2><3>, <2><4>,<2><5>, <2><6>,<3><1>, <3><2>, <3><3>, <3><4>, <3><5>, <3><6>,<4><1>, <4><2>, <4><3>, <4><4>, <4><5>, <4><6>,<5><1>, <5><2>, <5><3>, <5><4>, <5><5>, <5><6>,<6><1>, <6><2>, <6><3>, <6><4>, <6><5>, <6><6>.I’ve bolded the rolls that bring about a total of 7.

Step 2: Figure out the probability. The entire sample area is made up of 36 possible rolls. Tbelow are 9 rolls that bring about a 7, so the answer is:9/36 = .25.

Why not just Conduct Experiments all the Time?

Tright here are several factors why the field of Theoretical Probcapacity exists. Sometimes, conducting an experiment isn’t possible for useful or financial reasons. For instance, you might be researching a rare hereditary trait in salamanders and you desire to recognize what the probability of any type of one salamander having the rare trait is. If you don’t have access to all of the salamanders on the planet, you won’t have the ability to conduct an experiment so you’ll have to rely on theory to offer you the answer. Theoretical probcapability is also used in many type of locations of scientific research wright here direct experimentation isn’t possible. For example, probabilities entailing subatomic pwrite-ups or abstract frameworks choose vector spaces.


References

LeBlanc, D. (2004). Statistics: Concepts and Applications for Science, Illustrated Edition. Jones & Bartlett.

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CITE THIS AS:Stephanie Glen. "Theoretical Probability Definition and Examples" From piersonforcongress.com: Elementary Statistics for the rest of us! https://www.piersonforcongress.com/theoretical-probability/
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