A game at the state fair has a circular target with a radius

Question

Source: Economist GMAT 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. Ï€/9 D. Ï€^2/81 E. Ï€^2/9 The OA is D.

fskilnik@GMATH · Answer

BTGmoderatorLU wrote:Source: Economist GMAT 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 in random points on both throws, what is the probability that Jim won the game? A. 1/3 B. 1/9 C. Ï€/9 D. Ï€^2/81 E. Ï€^2/9 $$? = P\left( {2\,\,{\rm{hits}}\,\,{\rm{in}}\,\,{\rm{circular}}\,\,{\rm{region}}\,\,{\rm{in}}\,\,{\rm{two}}\,\,{\rm{throws}}} \right)$$ We may consider the similar figure(!) in which the radius of the circular target is 1cm and the square board has 3cm on a side. $$P\left( {1\,\,{\rm{hit}}\,\,{\rm{in}}\,\,{\rm{circular}}\,\,{\rm{region}}\,\,{\rm{in}}\,\,{\rm{one}}\,\,{\rm{throw}}} \right) = {{{S_{{\rm{circle}}}}} \over {{S_{{\rm{square}}}}}} = {{\pi \cdot {1^2}} \over {{3^2}}} = {\pi \over 9}$$ $$? = {\left( {{\pi \over 9}} \right)^2}\,\,\,{\rm{by}}\,\,{\rm{independency}}\,\,{\rm{on}}\,\,{\rm{throws}}$$ The correct answer is therefore (D). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.

Jay@ManhattanReview · Answer

BTGmoderatorLU wrote:Source: Economist GMAT 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. Ï€/9 D. Ï€^2/81 E. Ï€^2/9 The OA is D. Area of the circle = Ï€r^2 = Ï€*10^2 = 100Ï€ cm^2 Area of the square = 30*30 = 900 cm^2 Probability of hitting ONE dart within the circle = (Area of the circle) / (Area of the square) = 100Ï€ / 900 = Ï€/9 Probability of hitting both the darts within the circle = Ï€/9* Ï€/9 = Ï€^2/81 The correct answer: D Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Mehdipatnam GMAT Coaching | Madhapur GMAT Courses | Manhattan Review Hyderabad | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Scott@TargetTestPrep · Answer

BTGmoderatorLU wrote:Source: Economist GMAT 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. Ï€/9 D. Ï€^2/81 E. Ï€^2/9 T he area of the circular target of the board is 100ð�œ‹ cm^2 and the area of the entire board is 900 cm^2, so the probability of hitting the target once is 100ð�œ‹/900, or ð�œ‹/9. The probability of hitting the target twice is: ð�œ‹/9 x ð�œ‹/9 = ð�œ‹^2/81 Answer: D

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