Question

P(B)=2/3
P(A)=2/5
P(A or B)=11/20
Find P(A|B)

Answer 1

do you know another way to write P(A|B)?

Answer 2

Also do you recall:
\[P(A \text{ or } B)=P(A)+P(B)-P(A \text{ and } B) \\ \text{ and so } P(A \text{ and } B)=P(A)+P(B)-P(A \text{ or } B)\]

Answer 3

P(A|B)= P(A)•P(B)-P(A and B)

Answer 4

I believe so

Answer 5

shouldn't this be it:
\[P(A|B)=\frac{P(A \text{ and } B)}{P(B)}\]

Answer 6

Oh that as well yes

Answer 7

I'm a bit confused with the formulas

Answer 8

never seen the first one you mentioned
are you sure that is right?

Answer 9

I definitely seen the one I mentioned

Answer 10

I don't think I'm right but that is a formula for dependent overlap but I think I mixed my formulas up

Answer 11

No wait IM WRONG I WROTE IT WRONG DISREGARD 😅😅 sorry

Answer 12

k well try using the one I mentioned
try using both the ones I mentioned

Answer 13

like you find P(A and B) first using the first one I mentioned

Answer 14

then you can plug in that result a long with the number given for P(B)
to find P(A|B)

Answer 15

so first:
do you think you can find P(A and B)
using:
\[P(A \text{ and } B)=P(A)+P(B)-P(A \text{ or } B)?\]

Answer 16

Okay so the fraction forms would go in as

2/3+2/5-11/20

correct?

Answer 17

correct which equals

Answer 18

I'm a bit confused here though. Do I add the fractions even thought they do not have the same denominator?

Answer 19

to add/subtract fractions you need to find a common denominator first

Answer 20

Okay that's what confused me. Let me try..

Answer 21

31/60

Answer 22

k know use the second formula we mentioned
you just found P(A and B)
and you were already given P(B)
plug into the formula for P(A|B)

Answer 23

I cannot see the second formula you have given

Answer 24

\[P(A|B)=\frac{P(A \text{ and } B)}{P(B)}\]
you cannot see this one?

Answer 25

Wait yes I can now never mind

Answer 26

So it would kinda look like

X=31/60/2/3 correct?

Answer 27

\[P(A|B)=\frac{\frac{31}{60}}{\frac{2}{3}} \text{ or can be written as } \frac{31}{60} \cdot \frac{3}{2}\]

Answer 28

So the answer would be 93/120 or 0.775 correct?

Answer 29

yes
93/120 can be reduced
\[\frac{31}{60 } \cdot \frac{3}{2} =\frac{3}{60 } \cdot \frac{31}{2} =\frac{1}{20} \cdot \frac{31}{2}=\frac{31}{40}\]
so 31/40 or .775

Answer 30

Or 31/40 if simplified

Answer 31

Okay I understand now. Thank you so much!