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Each circle has center O. The radius of the smaller circle i

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Each circle has center O. The radius of the smaller circle i [#permalink] New post 13 Jun 2018, 22:09
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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. \(\frac{8}{9}\)
[Reveal] Spoiler: OA
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Re: Each circle has center O. The radius of the smaller circle i [#permalink] New post 13 Jun 2018, 22:19
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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.
Re: Each circle has center O. The radius of the smaller circle i   [#permalink] 13 Jun 2018, 22:19
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Each circle has center O. The radius of the smaller circle i

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