Answer:
[tex]Pr = \frac{9}{49}[/tex]
Step-by-step explanation:
Given
[tex]d = 28[/tex] --- big circle
[tex]A_2 = 36 \pi[/tex] --- area of small circle
Required
Probability that a point selected lands on the small circle
Calculate the area of the big circle using;
[tex]A_1 = \pi r^2[/tex]
Where
[tex]r = d/2[/tex]
So, we have:
[tex]r = 28/2 = 14[/tex]
This gives:
[tex]A_1 = \pi * 14^2[/tex]
[tex]A_1 = \pi * 196[/tex]
[tex]A_1 = 196\pi[/tex]
The probability that a point selected lands on the small circle is calculated by dividing the area of the small cicle by the big circle
This gives:
[tex]Pr = \frac{36\pi}{196\pi}[/tex]
[tex]Pr = \frac{36}{196}[/tex]
Simplify
[tex]Pr = \frac{9}{49}[/tex]
