Question

Two concentric circles are drawn having radii differing by 2 units. The probability that a point selected in the larger
circle does not lie in the smaller circle is 5/9. What is the radius of the smaller circle?​

Answer 1

Answer:

the answer for your question is up in the pictures

Answer 2

Given:

Two concentric circles are drawn having radii differing by 2 units. The probability that a point selected in the larger  circle does not lie in the smaller circle is 5/9.

To Find:

What is the radius of the smaller circle?​

Solution:

Let the radius of the larger circle be $r_{1}$ and that of the smaller circle be $r_{2}$

so we can say that

$r_{1}-r_{2}=2\\r_{1}=r_{2}+2$

now it is said that a point that will lie in the shaded region is 5/9 then from the attached image we can say that the value of the shaded region is 5x and that of the non-shaded region is 4x

now we can compare the areas of the two circles to find the values of r1 and r2

$\frac{\pi r_{1}^2}{\pi r{2}^2} =\frac{9x}{4x} \\\frac{r_{1}}{r_{2}} =\frac{3}{2} \\\frac{r_{2}+2}{r_{2}}=\frac{3}{2} \\r_{2}=4$

Hence, the radius of the smaller circle is 4 units.