Jamboree Question of the Day - Day 39, Dec 17th 2010

In the xy-plane, a triangle have vertex (0,0), (3,0) and (3,4). If point (a,b) is selected at random from the triangular region, what is the probability that b-a >0?

(A) 1/5

(B) 1/3

(C) 1/2

(D) 2/3

(E) 1/4

Solution (Posted on Dec 18th):

Answer: E

Area above y = x line in the triangle / area of triangle 

So y = x interest at (3,3). 

So area above = (½ * 3 * 4 – ½ * 3 * 3) / ½ * 3 * 4=¼