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# Probability Question

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I don't even know if this question makes any sense or not. I was asked by an individual I know, and couldn't give an answer as I'm not mathematically minded;

If there's a 70% chance of an event happening in the next 30 minutes, and there's a 15% chance of it happening in the next 5 minutes, then what's the overall probability?

Again, I don't know if it makes any sense or not, and haven't a clue to even approach it or determine it as wrong. I was wondering if anyone here could provide me with some clarification. :)

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The phrase “overall probability” is a bit too vague for me to comfortable answer a question about.

However given the 2 probability data in your example I can calculate one more datum:

Where $p_{(0,5)} = 0.15$ and $p_{(0,30)} = 0.7$

$p_{(5,30) = \frac{ p_{(0,30)} p_{(0,5)} }{ 1 -p_{(0,5)} } = \frac{ 0.7 \cdot 0.15 }{ 1 -0.15} } = \frac{11}{17} \dot= \,0.6471$

That is, the probability of the event happening between 5 and 30 min from now is about 64.71%

That’s all I can think of to derive from the given data.

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• 1 month later...

The phrase “overall probability” is a bit too vague for me to comfortable answer a question about.

' The summation can be interpreted as a weighted average, and consequently the marginal probability, , is sometimes called "average probability"; "overall probability" is sometimes used in less formal writings.' - http://en.wikipedia....ility#Statement

If there's a 70% chance of an event happening in the next 30 minutes, and there's a 15% chance of it happening in the next 5 minutes, then what's the overall probability?

This is a logic problem and with many logic problems the answer is in the question! The "overall probability" will be the same as, "a 70% chance of an event happening in the next 30 minutes". The "15% chance of it happening in the next 5 minutes" statement, only serves to complicate the the information given and distract you from the answer.

I think probabilities are usually presented as decimal numbers from 0(zero will never happen) to 1(one will actually happen), so the answer will be: 0.7 within 30 minutes.

Edited by phision

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