Sophia throws a dart at this square-shaped target: A square is shown with sides labeled 9. A shaded circle is shown in the center of the square. The diameter of the circle is 3.
Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)

Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)

Part A) The probability is closer to 0, because is less than 50%

Part B) The probability is closer to 1, because is greater than 50%

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

Part A) Is the probability of hitting the black circle inside the target closer to 0 or 1?

In this problem we have

x------> is the area of the black circle

y------> is the total area of the square target

Find the area of black circle

Find the total area of the square target

Find the probability

Convert to percentage

The probability is closer to 0, because is less than 50%

Part B) Is the probability of hitting the white portion of the target closer to 0 or 1?

In this problem we have

x------> is the area of the white portion of the target

y------> is the total area of the square target

Find the area of the white portion

The area is equal to the area of the square minus the area of the circle

Find the probability

Convert to percentage

The probability is closer to 1, because is greater than 50%