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# A game at the state fair has a circular target with a radius of 10 cm

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Retired Moderator
Joined: 29 Apr 2015
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A game at the state fair has a circular target with a radius of 10 cm  [#permalink]

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Updated on: 13 Jul 2015, 00:12
1
4
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Difficulty:

45% (medium)

Question Stats:

63% (01:15) correct 37% (01:19) wrong based on 172 sessions

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A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on both throws. If Jim hit the board on both throws, what is the probability that Jim won the game?

A. 1/3
B. 1/9
C. π/9
D. π^2/81
E. π^2/9

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Originally posted by reto on 12 Jul 2015, 06:14.
Last edited by Bunuel on 13 Jul 2015, 00:12, edited 1 time in total.
Edited the question.
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Re: A game at the state fair has a circular target with a radius of 10 cm  [#permalink]

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12 Jul 2015, 06:24
1
reto wrote:
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on both throws. If Jim hit the board on both throws, what is the probability that Jim won the game?

A. 1/3
B. 1/9
C. π/9
D. π2/81
E. π2/9

The probability of hitting the circular area = P(H) = favorable area/ total area = Area of the circle / Area of the square = $$\frac{\pi * 10^2}{30^2}$$ = $$\pi / 9$$

Thus for the player to win prizes = P(H) on the first throw * P(H) on the second throw =$$\pi/9 * \pi/9$$ = $${\pi ^2}/ {9^2}$$ = $${\pi ^2}/ {81}$$ . Thus D is the correct answer.
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Re: A game at the state fair has a circular target with a radius of 10 cm  [#permalink]

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13 Jul 2015, 00:11
reto wrote:
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on both throws. If Jim hit the board on both throws, what is the probability that Jim won the game?

A. 1/3
B. 1/9
C. π/9
D. π2/81
E. π2/9

Check other Probability and Geometry questions in our Special Questions Directory.

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Re: A game at the state fair has a circular target with a radius of 10 cm  [#permalink]

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31 Oct 2018, 17:29
reto wrote:
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on both throws. If Jim hit the board on both throws, what is the probability that Jim won the game?

A. 1/3
B. 1/9
C. π/9
D. π^2/81
E. π^2/9

The area of the circular target of the board is 100? cm^2 and the area of the entire board is 900 cm^2, so the probability of hitting the target once is 100?/900, or ?/9. The probability of hitting the target twice is:

?/9 x ?/9 = ?^2/81

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Re: A game at the state fair has a circular target with a radius of 10 cm &nbs [#permalink] 31 Oct 2018, 17:29
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