Single event probability equivalent to that of its permutations?

In summary, the conversation discusses the relationship between the probability of a specific event and the total probability of all its permutations within a set of events. It is concluded that the probability for a particular event is not necessarily equal to the total probability of its permutations. The conversation also involves the concept of permutations and their relationship to probability.
  • #1
Loren Booda
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4
Is the probability for a particular event, out of a set of events, equal to the total [normalized?] probability for all permutations of events from the set, including the particular event?

Say you have a 2 x 2 square with cells numbered 1 to 4. I am asking if the probability for square 1, p(1) is equal to the total probability for its permutations, p(1,2)+p(1,3)+p(1,4)+p(1,2,3)+p(1,2,4)+p(1,3,4)+p(1,2,3,4). Or should I divide this by the number of permutations?
 
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  • #2
Loren Booda said:
Is the probability for a particular event, out of a set of events, equal to the total [normalized?] probability for all permutations of events from the set, including the particular event?

The answer is almost surely no, whatever question you meant to ask. Just suppose that something has zero probability.

Say you have a 2 x 2 square with cells numbered 1 to 4. I am asking if the probability for square 1,

This doesn't make sense. I have a square with 4 numbers. This is nothing to do with probabilities.

p(1) is equal to the total probability for its permutations, p(1,2)+p(1,3)+p(1,4)+p(1,2,3)+p(1,2,4)+p(1,3,4)+p(1,2,3,4). Or should I divide this by the number of permutations?


How is P(1,2) a permution of P(1)?
 
  • #3
Consider this, demonstrable no doubt by the binomial theorem:

Given a set of events occurring with equal probability, the total number of permutations including a given event is one more than the total number of permutations without that event.
 
  • #4
I'll say it again: the total number of permutations of what?

There are 6 permutations of the numbers 1,2,3 and 4 permutations of 1,2. You know, n!, right? And again, probability has nothing to do with this fact.
 
  • #5
matt,

It turns out, upon further inspection, that what I was trying to describe is a redundancy. Sorry for the wild goose chase.
 

1. What is single event probability equivalent to that of its permutations?

Single event probability is the likelihood of a specific event occurring in a single trial or experiment. The probability of an event is equivalent to its permutations when there is only one possible outcome of the event. This means that the probability of the event is the same as the total number of possible outcomes.

2. How is single event probability related to permutations?

Single event probability is related to permutations because both concepts involve determining the number of possible outcomes in a given situation. In single event probability, we are interested in the likelihood of a specific outcome occurring, while in permutations, we are interested in the total number of possible arrangements or orders of a set of objects.

3. Can you give an example of single event probability equivalent to its permutations?

One example of single event probability equivalent to its permutations is when we toss a coin. The probability of getting heads or tails in a single toss is 1/2 (or 50%), and there are only two possible outcomes: heads or tails. Therefore, the probability of getting heads or tails is equivalent to the total number of permutations, which is also two.

4. How does the number of objects affect single event probability equivalent to its permutations?

The number of objects has a direct impact on single event probability equivalent to its permutations. As the number of objects increases, the number of possible outcomes or permutations also increases. This means that the probability of a specific outcome occurring decreases as the number of objects increases.

5. Why is understanding single event probability equivalent to its permutations important?

Understanding single event probability equivalent to its permutations is important because it helps us accurately calculate the likelihood of an event occurring in a single trial or experiment. It also allows us to make informed decisions and predictions based on the likelihood of certain outcomes. In addition, understanding permutations can help us in solving more complex probability problems involving multiple events.

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