Question

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!

Answer 1

we can do this i think

Answer 2

\[P(B|A)=\frac{P(A\cap B)}{P(A)}\]
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

Answer 3

\[P(A)=P(A|B)P(B) + P(A|B^c)P(B^c)\] 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
\[P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{P(A|B)P(B)}{P(A|B)P(B) + P(A|B^c)P(B^c)}\]

Answer 4

\[P(A^c\cap B^c)=P(A^c|B^c)P(B^c) P(B^c)=.7\times .65=.455\]

Answer 5

Are these independent events? if so, the P(A|B=P(A)

Answer 6

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.

Answer 7

a picture makes this much easier.

Answer 8

Well draw one then :P

Answer 9

thanks for your suggestions:)