# Thread: Probability of union

1. ## Probability of union

Hi,
LET Ai,Bi i=1,2 be sets such that the A's are independent and the B's are independent.
Also pr(Ai)<=pr(Bi),i=1,2

prove that Pr(A1UA2)<=Pr(B1UB2)

Thank's in advance.

2. ## Re: Probability of union

What is the formula for P(XUY) if X and Y are independent?

3. ## Re: Probability of union

I know the formula but how to proceed?

4. ## Re: Probability of union

Then please specifically answer Debsta's question!

5. ## Re: Probability of union

I will be glad for a clue to the solution.

6. ## Re: Probability of union Originally Posted by hedi Hi,
LET Ai,Bi i=1,2 be sets such that the A's are independent and the B's are independent.
Also pr(Ai)<=pr(Bi),i=1,2
prove that Pr(A1UA2)<=Pr(B1UB2) Originally Posted by hedi I know the formula but how to proceed? Originally Posted by HallsofIvy Then please specifically answer Debsta's question!
You were asked, even politely, to respond to a very simple request. Why the he** did you not? Or is it that you cannot? Originally Posted by hedi I will be glad for a clue to the solution.
Do not hold your breath. Answer the question.

7. ## Re: Probability of union

I am stuck with proving that x+y-xy<=u+v-uv when x<=uand
y<=v in (0,1).It is probably simple but somehow i dont come to a solution

8. ## Re: Probability of union Originally Posted by hedi I am stuck with proving that x+y-xy<=u+v-uv when x<=uand
y<=v in (0,1).It is probably simple but somehow i dont come to a solution
Thank you for finally replying. Now look at this very nice solution to a very tricky inequally. Originally Posted by Plato If $\large 0\le a\le x\le 1~\&~0\le b\le y\le 1$ then $\large a+b-a\cdot b\le x+y-x\cdot y$ Originally Posted by Idea $\displaystyle 1-a\geq 1-x \geq 0$

$\displaystyle 1-b\geq 1-y\geq 0$

Multiply

$\displaystyle (1-a)(1-b)\geq (1-x)(1-y)$
Multiply out both sides. Then multiply through by $-1$.