Chapter E, Problem 11.12EX

To determine

To find the probability that the point chosen at random lies inside the $\Delta AOB$ .

Answer to Problem 11.12EX

Option (d)

Explanation of Solution

Given information: Sector of the circle with radius 6 units and sector angle at ${90}^{°}$

  $\text{Area}\text{of}\text{the}\Delta AOB=\frac{1}{2}\times 6\times 6=18$

  $\text{Area of the circle}=36\pi$

The probability that a point chosen at random lies inside $\Delta AOB$ is $\frac{18}{36\pi }=\frac{1}{2\pi }$

Hence, the probability that a point lies inside the $\Delta AOB$ is $\frac{1}{2\pi }$