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Probability Old Exam P Forum

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Old 11-16-2015, 06:49 PM
tvossler tvossler is offline
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Default Conditional Probability

In general if P(A)>0, then P(B|A) = P(A and B)/P(A).

Sometimes, as in the case of SOA #17 from November 2001: The loss due to a fire in a commercial building is modeled by a random variable X with density function f(x) =.005(20-x) for 0<x<20

Given that a fire loss exceeds 8, what is the probability that it exceeds 16?

That conditional probability is shortened to P(B|A) =P(AandB)/P(A) = P(B)/P(A).

What is this due to? Why does it sometimes get reduced to this and other times not?

Thank you.
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Old 11-16-2015, 07:00 PM
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therealsylvos therealsylvos is offline
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When P(A and B) = P(B). If the loss is 16, it's certainly greater than 8. So P(Greater than 16 and greater than 8) = P(Greater than 16).
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Old 11-16-2015, 07:30 PM
tvossler tvossler is offline
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Thank you very much.
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Old 11-16-2015, 08:26 PM
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np
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Old 11-17-2015, 12:50 AM
KyleMoyer KyleMoyer is offline
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The best way to do it is write it out. If you write out "X > 8 and X > 16," you realize it looks kinda silly as opposed to (for example) "X > 8 and X < 16."

Granted, that's pretty straightforward, but you can get something a bit more involved where you write it out and realize it's redundant
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Old 11-17-2017, 04:47 PM
Z3ta Z3ta is offline
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If then .

Hence

I believe this is really common on exam problems.
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conditional probability, soa #17 november 2001

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