Answer: ![\frac{40}{49}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B49%7D)
Step-by-step explanation:
Given: The radius of the larger circle = 14 cm
The area of a circle is given by :-
![A=\pi r^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2)
The area of the larger circle will be :-
![A=\pi (14)^2=196\pi cm^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20%2814%29%5E2%3D196%5Cpi%20cm%5E2)
The radius of the smaller circle = 6 cm
The area of the smaller circle will be :-
![A=\pi (6)^2=36\pi cm^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20%286%29%5E2%3D36%5Cpi%20cm%5E2)
The area of the part which belongs to the the larger circle and outside the smaller circle =Area of larger circle- Area of smaller circle
![=196\pi-36\pi=160\pi cm^2](https://tex.z-dn.net/?f=%3D196%5Cpi-36%5Cpi%3D160%5Cpi%20cm%5E2)
Now, the probability that a point chosen at random in the given figure will be inside the larger circle and outside the smaller circle is given by:-
![\frac{160\pi}{196\pi}=\frac{40}{49}](https://tex.z-dn.net/?f=%5Cfrac%7B160%5Cpi%7D%7B196%5Cpi%7D%3D%5Cfrac%7B40%7D%7B49%7D)