Question

A point is randomly chosen in the diagram shown below.

A circle inside of a square. The circle touches all sides of the square.

What is the likelihood that a point chosen inside the square will also be inside the circle?

Answer 1

the answer is likely :)

Explanation:

Answer 2

The likelihood that a point chosen inside the square will also be inside the circle: 78.54%

Explanation:

• Let x is the side of the suqare

=> the area of the square is:
`x^(2)`

• Let d is the diameter of the circle

=> the area of the circle :
`(1)/(4) d^(2)`π

However, d=x because of the square property

<=> the area of the circle :
`(1)/(4) x^(2)`π

The likelihood that a point chosen inside the square will also be inside the circle:

the area of the circle / the area of the square

=
`(1)/(4) x^(2)`π /
`x^(2)`

=
`(1)/(4)` π *100%

= 0.7854 * 100%

= 78.54%