Question

Find the probability that a randomly selected point within the circle falls in the red shaded area (square). Round to the nearest tenth of a percent.​

Answer 1

Answer:

probability of selecting the square is 63.7% approximately

Step-by-step explanation:

First of all, the probability of the point of choice is within the red square can be obtained with this formula

probability = expected outcome / total number of possible outcomes

In this case, we are not dealing with discrete values which can be counted. instead, we are dealing with areas.

We are to go about this problem by finding the area of the internal square and dividing it by the area of the circle.

Area of the square

Area of the square = $l^2$

where length = $4\sqrt{2}$

Area = $(4\sqrt{2}) ^2 = 32cm^2$

Area of the circle

Area of the circle = $\pi r^2$

area of circle =$\pi \times 4^2 =50.26cm^2$

Probablity of selecting the square =

32/50.26 = 0.6366

To express this as a percentage, we multiply our answer by 100.

This will give us 0.6366 X 100 = 63.7% approximately