Question

nvolving sets A and B. Suppose for this problem that Pr[A|B]=1/2, Pr[A]=1/5, and Pr[B′]=7/10.
(1) What is Pr[B|A]?


(2) What is Pr[B|A′]?

Answer 1

hello again!

Answer 2

hi :)

Answer 3

you want \[P(A\cap B)\]right, so you can compute the ratio you need for both

Answer 4

\[\frac{P(A\cap B)}{P(B)}=P(A|B)\] you have two out of the three numbers you need to find \(P(A\cap B)\)

Answer 5

we have A and P[A|B]

Answer 6

you got \(P(B)\) and \(P(A|B)\) so you can solve for \(P(A\cap B)\)

Answer 7

We have the complement of B

Answer 8

but B = 3/10 Right?

Answer 9

yeah \[P(B)=\frac{3}{10}\]

Answer 10

'cause you be sippin syrup that's why!

Answer 11

so its (3/10)*(1/2)

Answer 12

hmm no

Answer 13

oh yes!

Answer 14

which is 4/5

Answer 15

now that is wrong

Answer 16

??

Answer 17

\[\frac{1}{2}\times \frac{3}{10}=\frac{3}{20}\]

Answer 18

my bad, im tired

Answer 19

oh the multiplication is wrong, yeah

Answer 20

so Pr(B|A)= 3/4

Answer 21

@satellite73 how would you do (2)

Answer 22

well i know A' is 4/5

Answer 23

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

Answer 24

but how do you Find P(A′∩B)

Answer 25

\[P(B)=P(A\cap B)\]

Answer 26

B= 3/10 and P(A∩B)=3/20

Answer 27

now what?

Answer 28

@satellite73 is the answer (3/10)/(4/5)= 3/8