Question

a circular target with a radius of 5 is inscribed in a square. if a point on the square is chosen at random what is the probability that the point is inside the square but outside the circle?

Answer 1

The probability that a point chosen at random on the square is inside the square but outside the circle is 0.215.

Step-by-step explanation:

The probability that a point chosen at random on the square is inside the square but outside the circle can be found by calculating the ratio of the area of the square that is not covered by the circle to the total area of the square.

The area of the square is given by the side length squared, which is equal to 2 times the radius (since the diameter of the circle is equal to the side length of the square). So, the area of the square is 2 * 5 * 2 * 5 = 100 square units.

The area of the circle is given by π times the radius squared, which is equal to π * 5 * 5 = 25π square units.

Therefore, the area of the square that is not covered by the circle is 100 - 25π square units.

The probability that a point chosen at random on the square is inside the square but outside the circle is equal to the area of the square that is not covered by the circle divided by the total area of the square:

Probability = (100 - 25π) / 100

Using an approximation for π, such as 3.14, we can calculate the probability:

Probability = (100 - 25*3.14) / 100 = 100 - 78.5 / 100 = 0.215