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16th KVJ Solutions7

Probability Introduction :

Here you find the solutions of  16th KVJ Solutions7 in detail explanation

7Q) A point 'A' is randomly chosen in a square of side length 1 unit. Find the probability that the distance from A to the centre of the square does not exceed x.

Solution:

            Please see the figure below.

 Let PQRS be a square of side 1 unit length.

 Let O be the center of square.

  Draw a circle with center O and radius x units.

 Let A be a point with in or on the circle with center O and radius x .

 Area of circle in which A lies = \(\prod * x^{2}\)

 Area of square PQRS =1*1=1

 Probability that the distance from A to the center of the square does not exceed x units = Area of circle/Area of square

                            =\(\frac{\prod * x^{2}}{1}\)

                            =\( \prod *x^{2}\)


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