Darts!

Probability Level 2

There is a circular dart board perfectly inscribed in a square board . Assuming that there is 100% probability that you will hit the square board with a dart, what is the probability in % that you will not hit the circular dart board ? ( π = 22 7 ) (\pi=\frac{22}{7})

Enter your answer in decimal upto three significant digits. You will not be penalised for too many significant digits


The answer is 21.428.

Muzaffar Ahmed by Muzaffar Ahmed , 21, India

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2 solutions

Muzaffar Ahmed
Mar 20, 2014

The probability that you will not hit the circular board is A r e a o f S q u a r e b o a r d − A r e a o f C i r c u l a r b o a r d A r e a o f S q u a r e B o a r d \frac{Area of Square board - Area of Circular board}{Area of Square Board}

Let the radius of the circle be x x , diameter and side of the square being 2 x 2x

Probability = = A ( S ) − A ( C ) A ( S ) \frac{A(S)-A(C)}{A(S)}

= ( 2 x ) 2 − π ( x ) 2 ( 2 x ) 2 = \frac{(2x)^2 - \pi(x)^2}{(2x)^2}

= 4 x 2 − π x 2 4 x 2 = \frac{4x^2 - \pi x^2}{4x^2}

= x 2 ( 4 − π ) 4 x 2 = \frac{x^2(4- \pi)}{4x^2}

= 4 − π 4 = \frac{4- \pi}{4}

= 4 − 22 7 4 = \frac{4- \frac{22}{7}}{4}

= 6 7 4 = \frac{ \frac{6}{7}}{4}

= 6 28 = \frac{6}{28}

= 600 28 = \frac{600}{28} %

= 21.428 = \boxed{21.428} %

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I answered 0.21428. F*ck. write in "%"

JejeRem JereRem - 7 years, 2 months ago

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I did that on purpose

Muzaffar Ahmed - 7 years, 2 months ago

just need more carefullness

Krisna Attayendra - 7 years, 2 months ago

same here lol

Jitesh Mittal - 7 years, 1 month ago

I had even simpler way of ding it.

Aditya Sai - 7 years, 2 months ago

You could just do this: Since r = s / 2 r = s/2 , A = π / 4 ⋅ s 2 A = \pi/4 \cdot s^2 . Thus the probability of not hitting the circular region is 1 − π 4 1-\frac{\pi}{4} .

Lee Wall - 7 years, 2 months ago

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Yes, that is correct, too..

Muzaffar Ahmed - 7 years, 2 months ago

Wow i made two consecutive mistakes and my rating dropped by 70 facepalm

Aayush Gupta - 7 years, 1 month ago
Amogh Jain
Mar 31, 2014

I used the same technique

0 Helpful 0 Interesting 0 Brilliant 0 Confused

i wrote 21.5 approximately

Prajwal Kavad - 7 years, 2 months ago

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