Question

Find the probability that a randomly selected point within the circle falls in the red shaded area (square)

Answer 1

Answer:

The probability that a randomly selected point within the falls in the shaded region is 0.6366

Step-by-step explanation:

Here in these cases probability, P=$\frac{n(E)}{n(S)}$=$\frac{required number of points}{Total number of points in sample space}$

And collection of points is nothing but the area occupied by those points

Therefore, P=$\frac{Required Area }{TotalArea Of Sample Space}$

Given: Radius, r=$4$ cm

           Side, s=$4\sqrt{2}$ cm

In this question, circle is the sample space,S, hence n(S)=area of the circle

                                                                                             =π$r^{2}$

                                                                                             =16π cm²

                                                                                             =50.265 cm²

Let A be the event of selecting a random point within the circle such that it falls within the shaded region

So, n(A)= area of the square

            =$s^{2}$

            =32 cm²

Therefore, the probability that a randomly selected point within the falls in the shaded region ,P(A)=$\frac{Area Of The Square}{Area Of The Circle}$=$\frac{32}{50.265} =0.6366$