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50) Good probability question

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by ern5231 » Wed May 12, 2010 1:31 am
A person wants to construct a circular pond within a rectangular boundary. The rectangular boundary has length=10 and width=8. The pond has the radius 1. If within the rectangular basin any point is taken as the center of the circle then what is the probability that the pool does not cross the boundary?

a) 0.5 b) 0.6 c) 0.7 d) 0.8
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by sanju09 » Wed May 12, 2010 1:58 am
ern5231 wrote:A person wants to construct a circular pond within a rectangular boundary. The rectangular boundary has length=10 and width=8. The pond has the radius 1. If within the rectangular basin any point is taken as the center of the circle then what is the probability that the pool does not cross the boundary?

a) 0.5 b) 0.6 c) 0.7 d) 0.8
The pond remains in the boundary as long as its center doesn't cross the white region shown above. Hence, out of a total region of 10 × 8 = 80 for the center of the pond to lie at, the favorable region is the white rectangle that is 8 × 6 = 48, and hence the required probability is 48/80 = [spoiler]3/5 or 0.6.

B[/spoiler]
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