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A square dart board has four dark circular regions of radius
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10 Dec 2020, 12:09
10 Dec 2020, 12:09
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74% (01:04) correct
25% (00:43) wrong based on 27 sessions
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GRE A square dart board has four dark circular regions.jpg [ 24.94 KiB | Viewed 1980 times ]
A square dart board has four dark circular regions of radius 3 inches as shown in the design above. Each point on the dart board is equally likely to be hit by a dart that hits the board. What is the probability that a dart that hits the board will his one of the circular regions?
A. \(\frac{\pi}{16}\)
B. \(\frac{\pi}{48}\)
C. \(\frac{\pi}{64}\)
D. \(\frac{1}{3}\)
E. \(\frac{1}{4}\)
Kudos for the right answer and explanation
Re: A square dart board has four dark circular regions of radius
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11 Dec 2020, 13:41
11 Dec 2020, 13:41
1
The area of one circular region is 9π but we have 4 so multiply that by 4 and we have 36π.
Next the area of the entire square is 576. (24*24)
Finally, we are asked of the probability that a dart will hit the area of the circular region so we apply the simple equation: Favourable outcome / Total outcome.
36π / 576 and that simplifies to π/16
Next the area of the entire square is 576. (24*24)
Finally, we are asked of the probability that a dart will hit the area of the circular region so we apply the simple equation: Favourable outcome / Total outcome.
36π / 576 and that simplifies to π/16
gmatclubot
Re: A square dart board has four dark circular regions of radius [#permalink]
11 Dec 2020, 13:41
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