Would someone please explain this problem to me? Thank you.
Set \(T\) consists of all points \((x, y)\) such that \(x^2 + y^2 = 1\) . If point \((a, b)\) is selected from set \(T\) at random, what is the probability that \(b \gt a + 1\) ?
(A) \(\frac{1}{4}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{3}{5}\)
(E) \(\frac{2}{3}\)
Source: GMAT Club Tests - hardest GMAT questions
Answer states that b> a+1 is in the upper left quartile because b=a + 1 (y=X+1) covers ponts -1,0 and 0,1, therefore b> a + 1 needs to be above that.
I understand it slightly but I'm not understanding the whole picture. The line b=a+1 that crosses pts -1,0 and 0,1 also is in lower left quartile and upper right quartile so why can't b>a+1 also be in those quartiles above the line?
Thank you.