Question

A game has a circular playing area in which you must hit a ball into a circular hole. The area of the playing area is 16 ft2. The hole has a diameter of 1 ft. What is the probability of hitting a ball into the circular hole? Express your answer as a percentage rounded to the nearest tenth.

Answer 1

You would have a 33% of hitting the target

Answer 2

Answer:

The probability of hitting a ball into the circular hole is 5%.                            

Step-by-step explanation:

Given : A game has a circular playing area in which you must hit a ball into a circular hole. The area of the playing area is 16 ft². The hole has a diameter of 1 ft.

To find : What is the probability of hitting a ball into the circular hole?

Solution :

Applying a geometric probability,

Deified as

$P =\frac{\text{Measured of region in the event}}{\text{Measured of entire region}}$

The entire region is the area of the circle,

The area of the playing area is 16 ft².

Region in the event is the area of the circular hole.

The hole has a diameter of 1 ft.

Radius of the hole is $\frac{1}{2}$ ft.

The area of the hole is $A=\pi r^{2}$

$A=\pi (\frac{1}{2})^{2}=\frac{\pi}{4}$

Substitute the value in the formula,

$P =\frac{\frac{\pi}{4}}{16}$

$P =\frac{\pi}{4\times 16}$

$P =0.049$

$P \approx 0.05$

or in percentage $P=5\%$

Therefore, The probability of hitting a ball into the circular hole is 5%.