Q:

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

Accepted Solution

A:
Answer:The probability that a randomly selected point within the falls in the shaded region is 0.6366Step-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 pointsTherefore, P=$$\frac{Required Area }{TotalArea Of Sample Space}$$Given: Radius, r=$$4$$ cm            Side, s=$$4\sqrt{2}$$ cmIn this question, circle is the sample space,S, hence n(S)=area of the circle                                                                                              =π$$r^{2}$$                                                                                              =16π cm²                                                                                              =50.265 cm²Let A be the event of selecting a random point within the circle such that it falls within the shaded regionSo, n(A)= area of the square             =$$s^{2}$$             =32 cm²Therefore, the probability that a randomly selected point within the falls in the shaded region ,P(A)=$$\frac{Area Of The Square}{Area Of The Circle}$$=$$\frac{32}{50.265} =0.6366$$