The probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is π/9 .
Probability of an event is defined as the Number of favorable outcomes divided by total number of outcomes.
It is denoted by P(E).
Given that
radius of circle = 3
side of the square = 9
Let E be the event that a randomly chosen point in the interior of the square will also lie in the interior of the circle
then
[tex]P(E)=\frac{AreaOfCircle}{AreaOfSquare}[/tex] ...(i)
Area of Circle = πr² = π(3)² = 9π
Area of Square = (side)²=(9)²=81
Substituting the values in equation (i) we get
[tex]P(E)=\frac{9\pi }{81}[/tex]
[tex]=\frac{\pi }{9}[/tex]
Therefore , the probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is π/9 .
The correct option is (C) π/9
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