H hedi Oct 2012 256 19 israel Feb 20, 2019 #1 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.

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.

D Debsta MHF Helper Oct 2009 1,286 587 Brisbane Feb 20, 2019 #2 What is the formula for P(XUY) if X and Y are independent?

H HallsofIvy MHF Helper Apr 2005 20,249 7,909 Feb 21, 2019 #4 Then please specifically answer Debsta's question! Reactions: 2 people

P Plato MHF Helper Aug 2006 22,462 8,634 Feb 21, 2019 #6 hedi said: 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) Click to expand... hedi said: I know the formula but how to proceed? Click to expand... HallsofIvy said: Then please specifically answer Debsta's question! Click to expand... You were asked, even politely, to respond to a very simple request. Why the he** did you not? Or is it that you cannot? hedi said: I will be glad for a clue to the solution. Click to expand... Do not hold your breath. Answer the question. Reactions: 1 person

hedi said: 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) Click to expand... hedi said: I know the formula but how to proceed? Click to expand... HallsofIvy said: Then please specifically answer Debsta's question! Click to expand... You were asked, even politely, to respond to a very simple request. Why the he** did you not? Or is it that you cannot? hedi said: I will be glad for a clue to the solution. Click to expand... Do not hold your breath. Answer the question.

H hedi Oct 2012 256 19 israel Feb 21, 2019 #7 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

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

P Plato MHF Helper Aug 2006 22,462 8,634 Feb 22, 2019 #8 hedi said: 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 Click to expand... Thank you for finally replying. Now look at this very nice solution to a very tricky inequally. Plato said: If $\large 0\le a\le x\le 1~\&~0\le b\le y\le 1$ then $\large a+b-a\cdot b\le x+y-x\cdot y$ Click to expand... Idea said: \(\displaystyle 1-a\geq 1-x \geq 0\) \(\displaystyle 1-b\geq 1-y\geq 0\) Multiply \(\displaystyle (1-a)(1-b)\geq (1-x)(1-y)\) Click to expand... Multiply out both sides. Then multiply through by $-1$. Last edited: Feb 22, 2019

hedi said: 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 Click to expand... Thank you for finally replying. Now look at this very nice solution to a very tricky inequally. Plato said: If $\large 0\le a\le x\le 1~\&~0\le b\le y\le 1$ then $\large a+b-a\cdot b\le x+y-x\cdot y$ Click to expand... Idea said: \(\displaystyle 1-a\geq 1-x \geq 0\) \(\displaystyle 1-b\geq 1-y\geq 0\) Multiply \(\displaystyle (1-a)(1-b)\geq (1-x)(1-y)\) Click to expand... Multiply out both sides. Then multiply through by $-1$.