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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

$\frac{1}{2}$
$\frac{π}{24}$
$\frac{π}{12}$
none of these

hint Hint:

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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