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MATHMAA

# 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:

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

=$$\frac{\prod * x^{2}}{1}$$

=$$\prod *x^{2}$$