Event independence little problem

[atrus_ovis]

Homework Statement

0<=x<=1 0<=,y <=1
event A: y<=x
event B: y<=1-x
Are events A,B independent?
Also, if B: x<=1/4 , are A,B independent?

The Attempt at a Solution

if independent,
P(A|B) = P(A)
P(A|B) = P(A)P(B) / P(A)P(B)+(1-P(A))P(B)
... ?

For B: x<=1/4 they are obviously dependent, as B normalizes the event space to the part
where x<=1/4, thus affecting the probability of A, since it involves x.
I can't express it mathematically though, in the formula.

 

[Mark44]

Homework Statement

0<=x<=1 0<=,y <=1
event A: y<=x
event B: y<=1-x
Are events A,B independent?
Also, if B: x<=1/4 , are A,B independent?

The Attempt at a Solution

if independent,
P(A|B) = P(A)
P(A|B) = P(A)P(B) / P(A)P(B)+(1-P(A))P(B)
... ?

For B: x<=1/4 they are obviously dependent, as B normalizes the event space to the part
where x<=1/4, thus affecting the probability of A, since it involves x.
I can't express it mathematically though, in the formula.

Graph the inequalities y <= x and y <= 1 - x. Both of these are regions in the plane. The graphs should show you whether events A and B are independent.

 

[atrus_ovis]

Hm,okay.Thank you.
And is this considered a legitimate answer?
Graphs, i mean.

 

[Mark44]

Well, the answer wouldn't be just a graph. You should say what it is that the graph represents as far as independence is concerned.

 

[atrus_ovis]

Yes, yes of course.
Thank you for your help Mark :)