Question

P, Q, R are the midpoints of the sides of triangle ABC. Another triangle is drawn by joining these points. A fine dot is placed into the figure without looking into the picture. What is the probability of falling the dot in triangle PQR? What is the probability of falling the dot outside the triangle?

Answer 1

Area of each small triangle is 1/4 of area of large triangle ABC.

Probability of the dot falling on triangle PQR is = 1/4

Probability of the dot falling on small triangle is = 1/4

Probability of the dot falling inside the triangle PQR is \(\frac{3}{4}-\frac{1}{4}=\frac{2}{4}=\frac{1}{2}\) less than that of outside the triangle.