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Question
Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1m?
Solution
Area of rectangle = l × b = 3 × 2 = 6 m2
Area of circle (of diameter 1 m) = `pir^2= pi((1)/2)^2 m^2= pi/4 m^2`
∴ Probability that the die will fall inside the
Cicle = `"Area of the favourable region"/ "Area of the whole region"`
= `"Area of the circle"/"Area of the rectangle"`
`= (pi/4)/6 = pi/4 xx 1/6 = pi/24`
P (die will land inside the circle) = `(pi/4)/6= pi/24`
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