Question

Conditional probability help.

Which of the following statements are true concerning two subsets A and B of sample space?

Answer 1

what do you think?

Answer 2

Well isn't B always a subset of A?

Answer 3

why would B have to be a subset of A?

Answer 4

Ohh wait, is it the other way around?

Answer 5

if you have two events (sets) they don't have to be subsets

Answer 6

lets focus on the the first one...do you think (A) is true or false?

Answer 7

What about supersets?

Answer 8

I think it is true

Answer 9

it is...why do you think that?

Answer 10

I can't really remember how my instructor explained it the other day, but it said something about if P(A) lying within P(B) and it being "collectively exhausted" or something along those lines..

Answer 11

so the P(A|B) says

The probability of A given B. So B has happened. So it is like throwing darts...I have hit B somewhere. If B lies inside of A then by hitting B I have also hit A. Thus P(A|B)=1 in this case

Answer 12

if x lands in B then it is also in A

Answer 13

Ohhh I see it clearly now. Visuals always help

Answer 14

So how about the rest?

Answer 15

It's A and B

Answer 16

correct

Answer 17

those are the ones that are always true

Answer 18

Alright, thanks man