About the naive definition of probability

In summary, during a conversation about a statistics introductory course, the topic of the naive definition of probability was discussed. It was mentioned that this definition requires equally likely outcomes and cannot handle an infinite sample space. The speaker also clarified that this means a biased coin cannot be modeled in this way. It was further explained that although this definition is important and basic, it has limitations and cannot be applied to all problems.
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red65
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hello, I took an introductory course about statistics, we viewed the naive definition of probability which says "it requires equally likely outcomes and can't handle an infinite sample space ", I understood that it requires finite sample space but I didn't understand "equally likely outcomes ", does it mean that if we have a coin with no equally likely heads and tales that do not satisfy the naive definition?
 
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  • #2
That's right, a biased coin cannot be modeled as two events, one heads and one tails, because in the naive model all events are equally likely.

You can kind of jam it in if you squint, e.g. ifthe coin is 2/3 to be heads, then have events H1 and H2 which are both the coin landing heads, and T which is the coin landing tails. But H1 vs H2 is not an observable difference.
 
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  • #3
ok, thanks a lot!
 
  • #4
You can call it "naive" but it is an important, basic subset of the problems. And many problems are a series of steps where each step is of that type. But it will not get you very far; there are too many problems that are not like that.
 
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Related to About the naive definition of probability

1. What is the naive definition of probability?

The naive definition of probability is a basic understanding that assumes all outcomes of an event are equally likely to occur. This means that the probability of an event is simply the number of favorable outcomes divided by the total number of possible outcomes.

2. How does the naive definition of probability differ from the mathematical definition?

The mathematical definition of probability takes into account all possible outcomes, including those that are not equally likely. It also considers the likelihood of each outcome occurring and assigns a numerical value between 0 and 1 to represent the probability of an event.

3. What are the limitations of the naive definition of probability?

The naive definition of probability assumes that all outcomes are equally likely, which is not always the case in real-world situations. It also does not consider the likelihood of each outcome, which can lead to inaccurate predictions.

4. How is the naive definition of probability used in everyday life?

The naive definition of probability is often used in situations where all possible outcomes are equally likely, such as flipping a coin or rolling a dice. It is also used as a basic understanding of probability before learning more advanced concepts.

5. Can the naive definition of probability be applied to more complex events?

While the naive definition of probability is a good starting point for understanding probability, it is not always applicable to more complex events. In these cases, the mathematical definition of probability is used to accurately calculate the likelihood of each outcome.

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