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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 circle with radius 0.5 m

A circle = (0.5)2 = 0.25πm2

Area of rectangle = 3 ×2=6m2

Probability (geometric) = (measure of specified region part)/(measure of whole region)

Probability that tie will land inside the circle with diameter 1m 

= (area of circle)/(area of rectangle) 

= 0.25πm2/6m2

= (1/4)x(π/6)

π/24

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