Probability & Frequency: Definition and Relationship

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In summary, frequency (or relative frequency) can be seen as an experimental measurement of probability. While over a small number of trials the relative frequency may differ considerably from the theoretical probability, over a large number of trials it should tend towards the theoretical probability. For example, in a coin tossing experiment, the theoretical probability of getting a "head" is 0.5, but after 10 tosses, the relative frequency may differ from this value. However, after a larger number of tosses, the relative frequency should become closer to the theoretical probability. The term "probability frequency" is not commonly used or defined, and it is possible that the conversation was referring to "probability density" or another related concept. It is important to be
  • #1
isabella
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Can anybody tell me what is the relationship between probability and frequency and hence what is the meaning of probabilty frequency.
 
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  • #2
Frequency (or more correctly relative frequency) could be considered an experimental measurement of probability. Over a small number of trials the relative frequence measurments may depart considerably from the theoretical probabilty, but over a large number of trials the relative frequence should tend toward the theoretical probabilty.

For example in a coin tossing experiment the theoretical probabilty of throwing a "head" is 0.5 if the coin is fair. If we throw the coin ten times then on average we'd expect to see heads occur five times, giving a relative frequence for heads equal to 5/10, the same as the theoretical probability.

Of course with only 10 tosses there is also a good chance that we'd see other than 5 heads and the relative frequence differ considerably from the probabilty. But if we tossed the coin say one thousand times then we'd expect the relative frequency to be much closer to the theroetical value.
 
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  • #3
So what is the meaning of probabilty frequency?
 
  • #4
isabella said:
So what is the meaning of probabilty frequency?

I assummed you were talking about "relative frequency" as applied to probability. Do you have a link or reference to somewhere the term "probability frequency" is used or defined?
 
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  • #5
Maybe, you mean "probability density"?
 
  • #6
i want to know if there a formula for frequentistic probability
 
  • #7
You should be more precise, the notions you are referring to, are not clear at all, perhaps, if English isn't your mother language then try and post these names in your language.
 

1. What is the definition of probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. How is probability related to frequency?

Probability and frequency are closely related because probability is based on the concept of frequency. The probability of an event is the long-term proportion of times that event would occur if the situation were repeated an infinite number of times.

3. Can probability be greater than 1?

No, probability cannot be greater than 1. This is because a probability of 1 means that an event is certain to occur, and a probability greater than 1 would imply that the event is even more certain to occur, which is not possible.

4. How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical definition of probability.

5. What is the difference between theoretical probability and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability, on the other hand, is based on actual data collected from experiments or real-life situations. It may differ from theoretical probability due to chance or other factors.

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