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A game of darts uses a square target with a circle inscribed inside
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12 Oct 2021, 08:20
12 Oct 2021, 08:20
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A game of darts uses a square target with a circle inscribed inside. What is the probability that a dart thrown at random lands inside the square but outside the inscribed circle?
A. 1-pi/2
B. 1-pi/4
C. 1-pi/5
D. 1-pi/6
E. 1-pi/8
A. 1-pi/2
B. 1-pi/4
C. 1-pi/5
D. 1-pi/6
E. 1-pi/8
A game of darts uses a square target with a circle inscribed inside
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12 Oct 2021, 09:31
12 Oct 2021, 09:31
1
RA911 wrote:
A game of darts uses a square target with a circle inscribed inside. What is the probability that a dart thrown at random lands inside the square but outside the inscribed circle?
A. 1-pi/2
B. 1-pi/4
C. 1-pi/5
D. 1-pi/6
E. 1-pi/8
A. 1-pi/2
B. 1-pi/4
C. 1-pi/5
D. 1-pi/6
E. 1-pi/8
Given: A circle is inscribed in \(a\) square. So if the side of Square is \(a\), then \(a\) is the diameter of circle.
Area of Circle = \(\frac{{\pi a^2}}{4}\)
Area of Square = \(a^2\)
Expected outcome is dart to land on the area that's out of circle but still within square, which is = \(a^2- \frac{{\pi a^2}}{4}\)
and probability of expected is Expected/Total outcome = \( (a^2 - \frac{\pi a^2}{4})/a^2= 1 - \frac{\pi}{4}\)
Answer is B)
gmatclubot
A game of darts uses a square target with a circle inscribed inside [#permalink]
12 Oct 2021, 09:31
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