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Catchfire
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Homework Statement
From Mathematical Statistics and Data Analysis 3ed, Rice
1.8 #61
Suppose chips are tested and the probability they are detected if defective is 0.95, and the probability they are declared sound if they are sound is 0.97. If 0.005 of the chips are faulty. What is the probability that a chip that is declared faulty is sound?
Homework Equations
P(A|B) = P(A[itex]\cap[/itex]B) / P(B)
P(A) = [itex]\Sigma[/itex]P(A|Bi)P(Bi)
The Attempt at a Solution
Let D- be the event a fault is detected
Let D+ be the event no fault is detected
Let Df be the event a chip is faulty
Let S be the event a chip is sound
P(D-|Df) = 0.95
P(D+|S) = 0.97
P(Df) = 0.005
P(S) = 1 - P(Df) = 0.995
Find P(S|D-) (the answer given is 0.86)
P(S|D-) = P(D-[itex]\cap[/itex]S) / P(D-) = P(D-|S)P(S) / P(D-)
So here's where I've been stuck.
First I'd like to know if I've translated the problem correctly.
Secondly how do I find P(D-|S) and P(D-) or am I going about this the wrong way?