Let's solve the problem step by step.

Given Information:

• The dartboard is a circle with a radius of 5 inches.

• The shaded region is a square with side length of 2 inches.

• Use π ≈ 3.14.

• The probability is given by:

  $P = \frac{\text{Area of shaded region}}{\text{Area of dartboard}}$

Step 1: Compute the Area of the Dartboard

The area of a circle is given by:

$A = \pi r^2$

Substituting $r = 5$ inches:

$A = 3.14 \times (5)^2 = 3.14 \times 25 = 78.5 \text{ square inches}$

Step 2: Compute the Area of the Shaded Square

Since the square has a side length of $2$ inches, its area is:

$A = 2 \times 2 = 4 \text{ square inches}$

Step 3: Compute the Probability

$P = \frac{\text{Area of shaded square}}{\text{Area of dartboard}}$

$P = \frac{4}{78.5} \approx 0.051$

Final Answer:

$\mathbf{0.05}$

Do you have any questions, or would you like a further breakdown?

Related Questions:

1. What is the probability if the side length of the shaded square were 3 inches instead?
2. How does changing the radius of the dartboard affect the probability?
3. What is the probability if the dartboard had a radius of 10 inches but the same shaded square?
4. How would the probability change if the shaded region were a circle instead of a square?
5. How do you convert between probability and percentage?

Tip: Always check the unit consistency in probability problems to avoid errors!