Question

Help! Suppose for this problem that Pr[A|B]=3/8 Pr[A]=9/20 Pr[B']=[3/5] What is Pr[B|A]?

Answer 1

Pr[B]=2/5 so I thought it would be
(2/5)/(9/20), but it says it's wrong!

Answer 2

what you are missing is only the probability of \(A\cap B\)

Answer 3

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

Answer 4

I thought A∩B = Pr[B] in this problem?

Answer 5

that is not usually the case
in fact it would only be true if B was contained in A so that \(A\cap B=B\)

Answer 6

A∩B=B∩A right? so 15/16??

Answer 7

btw do not confuse sets (for example \(A\cap B\) ) with numbers like \(P(A\cap B)\) they are different animals

Answer 8

\[\frac{P(A\cap B)}{P(B)}=P(A|B)\] means
\[P(A\cap B)=P(A|B)P(B)\] you know both the numbers on the right, so you can compute
\(P(A\cap B)\) by multiplication

Answer 9

Thank you! I get it!! Thank you so much!

Answer 10

you should expect that in general \(P(A\cap B)\) would be a rather small number, since it must be less than or equal to both \(P(A)\) and \(P(B)\)
unlikely it is \(\frac{15}{16}\)
in fact it is
\[P(A\cap B)=\frac{3}{8}\times \frac{2}{5}\]

Answer 11

yw

Answer 12

Wait, so how would I find P[B|A']? Since P(A'∩B)=P(A'|B)P(B), but I don't have P[A'|B]?

Answer 13

@satellite73 help please!!

Answer 14

got it! nvm

Answer 15

got it?

Answer 16

yep

Answer 17

good
you know a venn diagram really helps in these if you know how to fill it in and how to visualize it

Answer 18

yeah that's what I did!