Each circle has center O. The radius of the smaller circle is 2 and th

Question

circle_703.png 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. 1/9 B. 1/6 C. 2/3 D. 5/6 E. 8/9 Kudos for a correct solution .

AmoyV · Answer

Area of the whole circle=36(pi)

Area of the shaded region=36(pi)-4(pi)=32(pi)

Probability=32/36=8/9

Answer : E

Lucky2783 · Answer

Probability that point lies in smaller circle =  \frac{PI*2^2}{PI*6^2} = \frac{1}{9}

so probability that point lies in shaded region = 1 -1/9 = 8/9 
answer E

FightToSurvive · Answer

Area of the whole circle=6*6(pi)

Area of the shaded region=36(pi)-4(pi)=32(pi)

Probability=32/36=8/9

Hence E

bhatiavai · Answer

Area of larger circle = pi*(6)^2
Are of Smaller circle = pi*(2)^2
Area of Shaded region ==> Area of larger circle - Area of smaller circle
 pi(36-4)

Probability of the point being in shaded region = Ar of shaded region/Ar of Larger circle
 ==> 32pi/36pi = 8/9
Ans E

PareshGmat · Answer

Answer = E= 8/9

Area of big circle  = \pi6^2 = 36\pi

Area of shaded region  = 36\pi - 4\pi = 32\pi

Probability  = \frac{32\pi}{36\pi} = \frac{8}{9}

aj13783 · Answer

Probability of lying inside the shaded region = Area of Shaded region/Area of the larger circle

= Pi*(6^2 - 2^2)/Pi*6^2

= 32/36

= 8/9

Option E

Zhenek · Answer

Probability of the fact that the point lies in one of the sections is equal to the relation of the areas of the aforementioned section and the area of the whole thing, thus it has to be the relation of the shaded part's area to the whole area, which is easily found as  \frac{(36-4)\pi}{(36\pi)} = 8/9 
E

SavageBrother · Answer

Big circle radius: 6
Small circle radius: 2

Area big circle: 6^2 = 36
Area small circle: 2^2 = 4

36 - 4 = 32
32 / 36 =
8 / 9

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: Target_Probability.png

bumpbot · Answer

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Each circle has center O. The radius of the smaller circle is 2 and th

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Each circle has center O. The radius of the smaller circle is 2 and th

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