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Suppose you drop a tie at random on the rectangular region shown in fig. below. What is the probability that it will land inside the circle with diameter 1 m?

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Area of a circle with radius 0.5 m A circle = (0.5)2 = 0.25 πm2

Area of rectangle = 3 x 2 = 6m2

Probability (geometric) = \(\frac{measure\, of\, specified\, region\, part}{measure\, of\, whole\, region}\)

The probability that tie will land inside the circle with diameter 1 m

Therefore, the probability that the tie will land inside the circle = \(\frac{π}{24}\).

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