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anonymous

  • 4 years ago

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!

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  1. anonymous
    • 4 years ago
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    we can do this i think

  2. anonymous
    • 4 years ago
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    \[P(B|A)=\frac{P(A\cap B)}{P(A)}\] 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

  3. anonymous
    • 4 years ago
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    \[P(A)=P(A|B)P(B) + P(A|B^c)P(B^c)\] 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 \[P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{P(A|B)P(B)}{P(A|B)P(B) + P(A|B^c)P(B^c)}\]

  4. anonymous
    • 4 years ago
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    \[P(A^c\cap B^c)=P(A^c|B^c)P(B^c) P(B^c)=.7\times .65=.455\]

  5. Mertsj
    • 4 years ago
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    Are these independent events? if so, the P(A|B=P(A)

  6. anonymous
    • 4 years ago
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    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.

  7. anonymous
    • 4 years ago
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    a picture makes this much easier.

  8. Hero
    • 4 years ago
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    Well draw one then :P

  9. anonymous
    • 4 years ago
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    thanks for your suggestions:)

  10. anonymous
    • 4 years ago
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spraguer (Moderator)
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