Question

Sherwin throws a dart at this square-shaped target:

Part A: is the probability of hitting the black circle inside the target closer to 0 or 1? Why?

Part B: is the probability of hitting the white portion of the target closer to 0 or 1? Why?

Answer 1

PartA.
`P_c = 0.0267`

PartB.
`P_b = 0.9733`

Explanation:

To answer this question we must find the area of the square and the area of the circle.

The area of the circle is:

`A_c = \pi r^2`

Where r is the radius, and: r = diameter/2 and the diameter = 4

So:

`r = 2`

Therefore the area
`A_c` of the circle is:

`A_c = \pi(2)^2\\\\A_c = 12.566`

Then, the area of the square is:

`A_b = 22^2 -A_c`

`A_b = 22^2 - 12.566`

`A_b = 471.434`

Part A

The probability
`P_c` that the dart falls within the black circle is:

`P_c = (A_c)/(A_b)`

`P_c = (12.566)/(471.434)`

`P_c = 0.0267`

The probability is much closer to 0 than to 1

Part B.

The probability
`P_b` that the dart falls within the white area is:

`P_b = 1-P_c\\\\P_b = 1-0.0267\\\\P_b = 0.9733`

The probability is much closer to 1 than to 0. This is because the area of the black circle is much smaller than the white area, therefore it is more difficult for the dart to hit the black circle.