## 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!

1. anonymous

we can do this i think

2. 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

3. 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 $P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{P(A|B)P(B)}{P(A|B)P(B) + P(A|B^c)P(B^c)}$

4. anonymous

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

5. Mertsj

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

6. 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.

7. anonymous

a picture makes this much easier.

8. Hero

Well draw one then :P

9. anonymous