Question

suppose event A is included in (that is, is a subset of) event B. Then P(A and B) = P(B)
True or False?

Answer 1

If A is a subset of B, then we can visually represent it like this

Answer 2

now if you're in both sets A and B, then you are here

Answer 3

is that the same as being in set B (all of set B)?

Answer 4

Yes

Answer 5

depends on of A is defined as a "proper" subset, or just as a subset

Answer 6

it says its just a subset

Answer 7

but if you're in set B, you could be out here

Answer 8

so there is no guarantee that P(A and B) = P(B)

Answer 9

oh I see

Answer 10

the only way for P(A and B) = P(B) to be true is if A = B

Answer 11

at best: P(AnB) = P(A)

if P(A) = P(B), which can occur of A is a subset of B (B is a subset of itself after all) but this is a special case

Answer 12

okay I get it now thanks guys!

Answer 13

yw