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Circles X and Y are concentric. If the radius of circle X is three  [#permalink]

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6 00:00

Difficulty:   15% (low)

Question Stats: 78% (01:37) correct 22% (01:46) wrong based on 136 sessions

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Circles X and Y are concentric. If the radius of circle X is three times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?

(A) 13

(B) $$\frac{\pi}{3}$$

(C) $$\frac{\pi}{2}$$

(D) 5/6

(E) 8/9

Originally posted by guerrero25 on 26 Jun 2013, 03:11.
Last edited by guerrero25 on 26 Jun 2013, 03:26, edited 1 time in total.
Math Expert V
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Posts: 59012
Circles X and Y are concentric. If the radius of circle X is three  [#permalink]

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1
guerrero25 wrote:
Circles X and Y are concentric. If the radius of circle X is three times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?

(A) 13

(B) $$\frac{\pi}{3}$$

(C) $$\frac{\pi}{2}$$

(D) 5/6

(E) 8/9

Say the radius of the smaller circle (Y) is 1, then the radius of the larger circle would be 3.

The area of X = $$\pi{R^2}=9\pi$$;
The area of Y = $$\pi{r^2}=\pi$$.

The probability = (Favorable)/(Total) = $$\frac{9\pi-\pi}{9\pi}=\frac{8}{9}$$.

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Re: Circles X and Y are concentric. If the radius of circle X is three  [#permalink]

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Small circle radius = a, so area = PI a ^ 2

Large circle radius = 3a, so area = 9. PI a ^ 2

Area of shaded region = 9PI a^2 - PI a^2 = 8 PI a^2

So, probability = ( 8 PI a^2 ) / (9 PI a^2 )

= 8/9 = Answer = E
Attachments circle.JPG [ 7.89 KiB | Viewed 1695 times ]

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Re: Circles X and Y are concentric. If the radius of circle X is three  [#permalink]

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_________________ Re: Circles X and Y are concentric. If the radius of circle X is three   [#permalink] 20 Jan 2018, 08:58
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# Circles X and Y are concentric. If the radius of circle X is three  