Maths-
General
Easy

Question

Suppose you drop a die at random on the rectangular region shown. The probability that it will land inside the circle with diameter 1m is

  1. fraction numerator 1 over denominator 2 end fraction    
  2. fraction numerator pi over denominator 24 end fraction    
  3. fraction numerator pi over denominator 12 end fraction    
  4. none of these    

hintHint:

Probability(Event) = Favorable Outcomes/Total Outcomes . Here, Favorable out come will be the area of circle with diameter 1 m and Total out come will be total are of rectangle and event is landing of dice in the circle.

The correct answer is: fraction numerator pi over denominator 24 end fraction


    Here, Favorable out come will be the area of circle with diameter 1 m and Total out come will be total are of rectangle and event is landing of dice in the circle.
    So. area of circle with diameter =πd squared over 4 space equals space fraction numerator pi left parenthesis 1 right parenthesis squared over denominator 4 end fraction space equals straight pi over 4 space m squared space left parenthesis G i v e n comma space d space equals space d i a m e t e r space equals space 1 m space right parenthesis
    Area of rectangle with dimension 3m and 2 m is 3*2 = 6 m2 .
    Probability( landing of dice in the circle) = Area of circle /Area of rectangle
    fraction numerator space begin display style straight pi over 4 end style space over denominator 6 end fraction space equals space straight pi over 24
    Therefore, The probability that it will land inside the circle with diameter 1m is fraction numerator pi over denominator 24 end fraction.

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