Question

if 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?

Answer 1

The number of points that are expected to lie inside the circle is 785.

A circle is a closed two-dimensional figure. In a circle, all points are equidistant from the centre.

As per the given question, the circle is inscribed in a square,

• The radius of the circle ( r )   =   1
• The side length of the square ( s )   =   2

⇒ The area of the circle   =   π × r × r

                                           =   π × 1 × 1

∴ The area of the circle    =   π

⇒ The area of the square   =   s × s

                                             =   2 × 2

∴The area of the square    =    4  

The probability that a randomly selected point inside the square will lie inside the circle,

p   =   π / 4

The probability that a randomly selected point inside the square will lie outside the circle,

q   =  1 - p

q   =  1 - ( π / 4 )

⇒ Binomial trial with n   =   1000 and  p   =   π / 4,

Number of points expected to lie inside the circle(N)  =   n × p

                                                                                         =   1000 × ( π / 4 )

                                                                                         =   1000 × ( 3.14 / 4 )

                                                                                         =   1000 × ( 0.785 )

                                                                                  N    =   785  

Therefore, 785 expected points lie inside the circle.  

To know more about circles refer to:

https://brainly.com/question/24810873

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The complete question is