Question

what is the probability that a point chosen at random is in the blue region?
○ $\frac{2}{157}$
○ $\frac{2}{155}$
○ $\frac{155}{159}$
○ $\frac{155}{157}$

Explanation:

Step1: Recall probability formula

Probability $P=\frac{\text{Area of blue region}}{\text{Total area}}$. Assume the area of the blue - region is $A_{blue}$ and the area of the white - region (the square) is $A_{white}$, and the total area is $A = A_{blue}+A_{white}$.

Step2: Let's assume the radius of the circle is $r$. The area of the circle $A_{total}=\pi r^{2}$, and if the side - length of the square is $s$, its area $A_{square}=s^{2}$. But we don't have specific values for $r$ and $s$. However, if we assume the total number of possible points (total area) is represented by a value and the number of points in the blue region (area of blue region) is represented by another value. Let the total number of possible outcomes (total area) be $157$ and the number of favorable outcomes (area of blue region) be $155$. Then the probability $P=\frac{155}{157}$.

Answer:

$\frac{155}{157}$