The area of the shaded circle below is 78.5 square inches. The area of the large circle is 314 square inches.

Question

A shaded circle is inside of a larger unshaded circle.

What is the probability that a point chosen at random will be in the shaded region? Round the answer to two decimal places.
0.25
0.33
0.66
0.75

Answer 1

To find the probability that a randomly chosen point will be in the shaded region, we can use the formula:

\[ \text{Probability} = \frac{\text{Area of Shaded Region}}{\text{Area of Large Circle}} \]

Given:

• Area of the shaded circle = 78.5 square inches
• Area of the large circle = 314 square inches

Now, we can substitute the values into the formula:

\[ \text{Probability} = \frac{78.5}{314} \]

Now, we compute the fraction:

\[ \text{Probability} \approx 0.2508 \]

Rounding this to two decimal places gives:

\[ 0.25 \]

Thus, the probability that a point chosen at random will be in the shaded region is:

\(\boxed{0.25}\)