Question

If a point is chosen inside the square, what is the probability that it will also be inside the circle?

Answer 1

`79\%`

Explanation:

The probability that the point is chosen in the circle is equal to the area of the circle divided by the area of the square.

Formulas used:

• Area of a square with side length
  `s` is given by
  `A=s^2`
• Area of a circle with radius
  `r` is given by
  `A=r^2\pi`

The segment marked as 1 represents not only the radius of the circle, but also half the side length of the square. Therefore, the side length of the square is 2, and we have:

Area of square:
`A=2^2=4`

Area of circle:

`A=1^2\pi=\pi`

Therefore, the probability that the point will be inside the circle is:

`(\pi)/(4)=0.78539816339\approx \boxed{79\%}`