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Does physics or mathematics allow for a probability of a probability?

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- Thread starter Loren Booda
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- #1

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Does physics or mathematics allow for a probability of a probability?

- #2

mathman

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- #3

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For instance, if an event has a probability

- #4

Hurkyl

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For events A and B, if:

P(A) = μ

P(B | A) = ν (that's probability that B occurs, given that A occurs)

P(A | B) = 1 (B can only occur if A occurs)

Then we can apply the formula

P(A|B) P(B) = P(B|A) P(A)

to get

P(B) = μ ν

- #5

jcsd

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I throw a coin four times, the probailty that I get three heads is 0.25, but you can also say: The probabilty that the probailty after the second throw is 0.0625 is 0.5.

- #6

jcsd

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And has Hurkyl says, my example is a conditonal probabilty.

- #7

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Could you recommend a simple online source for conditional probability, Hurkyl? The notation slips me.

- #8

NateTG

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Jeff Hornachek (Don't remember spelling) had a 90% free throw rate, so on a double free throw, he had a 81% (or 90% of 90%) chance of making his second shot.

An alternative example would be from statistics or zero knowledge proofs where probability is used as an expression of confidence. Be wary that this type of double probability is something different than the conditional probalitity described above.

For example, there is a 90% probability that that loaded die has a 70% chance of rolling a 6.

Or from polling: There is a 95% probability (expressing confidence in the poll) that each voter has a 45% probability of voting for Arnie.

- #9

Hurkyl

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- #10

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A Gaussian curve might be described as an infinite succession of probabilities, whereas a constant statistic could not. Endless deviatives of the Gaussian attest to the potential underlying infinite series of probabilities.

- #11

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http://plato.stanford.edu/entries/bayes-theorem/

Steve

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