1. EXAMPLE 3 Use areas to find a geometric probability The diameter of the target shown at the right is 80 centimeters. The diameter of the red circle on the target is 16 centimeters. An arrow is shot and hits the target. If the arrow is equally likely to land on any point on the target, what is the probability that it lands in the red circle? ARCHERY

2. EXAMPLE 3 Use areas to find a geometric probability SOLUTION Find the ratio of the area of the red circle to the area of the target. P (arrow lands in red region) = Area of red circle Area of target = (8 2 ) (40 2 ) = 64 1600 = 1 25 The probability that the arrow lands in the red region is 1 25, or 4%. ANSWER

3. EXAMPLE 4 Estimate area on a grid to find a probability SCALE DRAWING Your dog dropped a ball in a park. A scale drawing of the park is shown. If the ball is equally likely to be anywhere in the park, estimate the probability that it is in the field. SOLUTION STEP 1 Find the area of the field. The shape is a rectangle, so the area is bh = 10 3 = 30 square units.

4. EXAMPLE 4 STEP 2 Find the total area of the park. Make groups of partially covered squares so the combined area of each group is about 1 square unit. The total area of the partial squares is about 6 or 7 square units. So, use 52 + 6.5 = 58.5 square units for the total area. Estimate area on a grid to find a probability Count the squares that are fully covered. There are 30 squares in the field and 22 in the woods. So, there are 52 full squares.

5. EXAMPLE 4 STEP 3 Write a ratio of the areas to find the probability. Estimate area on a grid to find a probability P (ball in field) = Area of field Total area of park = 300 585 = 20 39 30 58.5 The probability that the ball is in the field is about 20 39, or 51.3%. ANSWER

6. GUIDED PRACTICE for Examples 3 and 4 6. In the target in Example 3, each ring is 8 centimeters wide. Find the probability that an arrow lands in a black region. 14 25 = 56% ANSWER

7. GUIDED PRACTICE for Examples 3 and 4 7. In Example 4, estimate the probability that the ball is in the woods. or about 48.7%. 19 39 ANSWER