Question

What is the likelihood that a point chosen inside the square will also be inside the circle ?It Chose one : A. is impossible ,B. it is unlikely, C it is likely D. it is certain

Answer 1

Answer:

C. It is likely

Step-by-step explanation:

Given

See attachment for diagram

For the square.

Let

$Length = L$

So, the area is:

$Area = Length^2$

$A_1=L^2$

The side length of the square equals the diameter of the circle.

So:

$diameter (d) = L$

The radius is:

$r = \frac{1}{2}d$

$r = \frac{1}{2}L$

The area is:

$Area = \pi r^2$

$A_2 = \pi * (\frac{1}{2}L)^2$

$A_2 = \pi * \frac{1}{4}L^2$

$A_2 = \frac{22}{7} * \frac{1}{4}L^2$

$A_2 = \frac{22}{28} L^2$

The likelihood that a point will be common to the square and the circle is:

$Pr = \frac{A_2}{A_1}$

$Pr = \frac{\frac{22}{28} L^2}{L^2}$

$Pr = \frac{22}{28}$

$Pr = 78.57\%$

The above probability is greater than 50% but less than 100%.

Hence, it is likely