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Director  Joined: 07 Jan 2018
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Kudos [?]: 544 , given: 88

Each circle has center O. The radius of the smaller circle i [#permalink] 00:00

Question Stats: 75% (00:55) correct 25% (01:40) wrong based on 4 sessions
Attachment: circle.png [ 7.36 KiB | Viewed 502 times ]

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 GRE Forum Moderator
Joined: 29 May 2018
Posts: 125
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Kudos [?]: 85  , given: 4

Re: Each circle has center O. The radius of the smaller circle i [#permalink]
1
KUDOS
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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