anonymous
  • anonymous
hi. if A is the event that a lie detector test says that a given person is lying. B is that the person is truly lying. only information provided is: P(A|B) = 0.85 P(not A|not B ) = 0.70 P(B) = 0.35. what is P(B|A) ? thanks for your help!
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
we can do this i think
anonymous
  • anonymous
\[P(B|A)=\frac{P(A\cap B)}{P(A)}\] so we need these numbers on the right. now we know that \[P(A\cap B)=P(A|B)P(B)=.85\times .35=.2957\] so all we need is the denominator \[P(A)\] to be done
anonymous
  • anonymous
\[P(A)=P(A|B)P(B) + P(A|B^c)P(B^c)\] and we know 3 out of these 4 numbers we just don't know \[P(A|B^c)\] btw i bet this is under the heading of Baye's formula which is \[P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{P(A|B)P(B)}{P(A|B)P(B) + P(A|B^c)P(B^c)}\]

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anonymous
  • anonymous
\[P(A^c\cap B^c)=P(A^c|B^c)P(B^c) P(B^c)=.7\times .65=.455\]
Mertsj
  • Mertsj
Are these independent events? if so, the P(A|B=P(A)
anonymous
  • anonymous
no i don't think they are independent, buy we could check. in any case we see from the above that \[P(A)=.4925\] and so we are done.
anonymous
  • anonymous
a picture makes this much easier.
Hero
  • Hero
Well draw one then :P
anonymous
  • anonymous
thanks for your suggestions:)
anonymous
  • anonymous

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