amorphous wrote:

Each circle has center O. The radius of the smaller circle is 2 and the radius of the larger circle is 6. If a point is selected at random from the larger circular region, what is the probability that the point will lie in the shaded region?

A. \(\frac{1}{9}\)

B. \(\frac{1}{6}\)

C. \(\frac{2}{3}\)

D. \(\frac{5}{6}\)

E. \(\frac{8}{9}\)

Total area of larger circle is 36*pi.

Area of smaller circle is 4*pi.

Now To get the area of shaded part ,we need to separate total area - smaller area = 32pi ( 36pi - 4pi).

Now to get the probability for the shaded part we need to take entire area of the maximum circle in the denominator.

Since p(a) = expected records / Total records.

i.e shaded / full circle => 32pi / 36pi => 8/9.

E.