Answer:
25%.
Step-by-step explanation:
First, let's find the area of both circles. The area of a circle is given by:
[tex]\displaystyle A = \pi r^2[/tex]
The radius of the smaller circle is one. Thus, its area is:
[tex]\displaystyle A = \pi (1)^2 = \pi[/tex]
The radius of the larger circle is two. Thus, its area is:
[tex]\displaystyle A = pi (2)^2 = 4\pi[/tex]
The probability that a random point chosen will be inside the small circle will be the area of the small circle over the total area. Hence:
[tex]\displaystyle P= \frac{\pi }{4\pi}=\frac{1}{4}= 25\%[/tex]
The probability of a random point being in the small circle is 25%.
