M and N are the midpoints of opposite sides of square ABCD.A point is selected at random in the square.find the probability that it lies in traingle ADM but not in triangle ADN

Answer 1

I picked M as the midpoint of AB, and N as the midpoint of DC
let P be the intersection of AN and DM

in triangle ADM but not in triangle ADN
--> triangle AMP

by simple ratio calculations, the area of triangle AMP = (1/8)the square.

so prob(of your event) = 1/8