Question

M and N are midpoints of opposites of square ABCD.

A point is selected at random in the square. Find the probability that it lies in:
a)∆ADM
b)∆ADM but not in ∆ADN.
c) neither in ∆ADM nor in ∆ADN

Answer 1

Explanation:

a) The probability that the point selected at random lies in ∆ADM is 1/4. This is because ∆ADM is one of the four equal parts of the square ABCD.

b) The probability that the point selected at random lies in ∆ADM but not in ∆ADN is 1/8. This is because ∆ADM and ∆ADN are two of the four equal parts of the square ABCD, and the union of these two parts forms one quarter of the square. Hence, the probability of the point lying in one of these parts but not in the other is 1/8.

c) The probability that the point selected at random lies neither in ∆ADM nor in ∆ADN is 3/4. This is because the union of ∆ADM and ∆ADN forms one quarter of the square ABCD, while the remaining three quarters of the square lie outside of both ∆ADM and ∆ADN. Hence, the probability that the point lies outside of both these parts is 3/4.