Question

Find the probability that a randomly placed point falls within the smaller, inner circle.

Answer 1

Answer:

The probability that a randomly placed point falls within the smaller, inner circle is 25/64

Step-by-step explanation:

The remaining part of question is attached

Solution

The area of smaller circle is

$\pi r^2 = 25 \pi$

The area of large circle is

$\pi r^2 = 64 \pi$

Area of the shaded region

Area of large circle - area of small circle

$64\pi -25\pi = 39\pi$

Probability that the point falls in the region of smaller circle is

$\frac{25\pi }{64\pi } \\\frac{25}{64}$