Question

Suppose that P(A)=0.41, P(C∣A)=0.005, and P(C′∣A′)=0.008. Find P(A∣C).

Answer 1

baye's formula right?

Answer 2

so you know how to use it or should we go through step by step?

Answer 3

*do you know how to use it?

Answer 4

Yes, but I'm confused with the C' and A', that part throws me off. I understand it without the primes, but with them it's confusing.

Answer 5

you want \(P(A|C)\) which is by definition
\[\frac{P(A\cap C)}{P(C)}\]

Answer 6

you need to find \(P(C)\) and \(P(A\cap C)\)
the second one is easy, because
\[P(A\cap C)=P(A)\times P(C|A)\] and you know both of those numbers

Answer 7

Okay, so P(A∩C)= .00205

Answer 8

yes

Answer 9

now you need \(P(C)\) and that takes some work

Answer 10

great

Answer 11

not much work though

Answer 12

Alright, how do i do it

Answer 13

give me a second i think i can come up with an easy way

Answer 14

yes, lets make it easy by drawing a venn diagram
first off \(P(A')=1-.41=.59\) is a no brainer

Answer 15

then
\[P(A'\cap C')=P(C'|A')\times P(A')=.008\times .59=.00427\]

Answer 16

now it should be easy to find \(P(C)\) since it all has to add up to 1
is it clear how i filled out the diagram?

Answer 17

It does, but does the entire thing have ot add up to one or just the circles?

Answer 18

the entire thing
that is why we needed \(P(A'\cap C')\) it is what is outside the two circles

Answer 19

i get \(1-.41-.00427 = 0.58573\)

Answer 20

So C would = .58573, and then you'd take .00205/.58573

Answer 21

aaannnd it says that answers wrong