Question

Show that if A and B are two independent events and A is a subset of B, then either P(A) = 0 or P(B) = 1.

Answer 1

@inkyvoyd

Answer 2

\[p(a \Omega b)=p(a).p(b)\]
\[p(aUb)=p(a)=p(a)+p(b)-p(a).p(b)->p(b).(1-p(a))=0\]
p(a)=1 or p(b)=0

Answer 3

thanks! can you answer 1 more question please?

Answer 4

p(AUB)=p(B)

Answer 5

just change it p(a)=0 or p(b)=1

Answer 6

ok. Thank you. you ve been a great help!

Answer 7

you are welcome

Answer 8

The other question is:
Show that if P(A|B) >= P(B|A) then P(A)<=P(B) is false

Answer 9

\[p(a|b).p(b)=p(b|a).p(a)=p(ab)->p(a)=[p(a|b)/p(b|a)].p(b)\]
\[p(a|b)/(p(b|a))\ge1\]
->\[p(a) ge p(b)\]

Answer 10

\[p(a)\ge p(b)\]

Answer 11

so it's false

Answer 12

sorry, what is what is gep?

Answer 13

and does P(B|A) imply that A and B are independent or just simply imply that A and B intersect?

Answer 14

greater or equal

Answer 15

only if p(B|A)=p(B)

Answer 16

oh i see...how do i show that the next part of the question is false:
If P(A complement) = a and P(B complement) = b then P(AUB) < 1-a-b is false because P(AUB) <=2-a-b?

Answer 17

A and B are independent?

Answer 18

the question doesnt say...