Page 833 - Algebra 1

Example
2
Finding Geometric Probability with Circles
A target is made of two concentric circles. The outer circle has a radius of 12 inches. The inner circle has a radius of
4 inches. What is the probability that a dart will land in the inner circle?
total outcomes
4 in
favorable outcomes = shaded area ____
=
π(4)
Use A = πr Simplify.
2
to find the areas.
entire area _ 2
π(12)2
__ 144π 9
= 16π = 1
The probability that a dart will land in the inner circle is _1 . 9
Recall that the formula for the complement of an event is: 1 - P(A) = P(not A)
Finding the Probability of the Complement
12 in
Hint
When finding the ratio of the areas of two circles, leave the areas in terms of π to make simplification easier.
SOLUTION
Example
3
Math Language
The complement of an event is all the outcomes in the sample space that are not included in the event.
a. A town is represented by a circle with a diameter of 50 miles. There is a square park with side length 5 miles located within the town. What is the probability that a raindrop would land in the town, but not the park?
SOLUTION
5 miles
Find the probability of the complement of the raindrop landing in the park. P(not landing in the park) = 1 - P(landing in the park)
= 1 - area of park __
_area of town
52
= 1 - 2
_π(25) = 1 - 25
625π
The probability of a raindrop landing in the town but not the park is 99%.
≈ 0.99
b. A carnival game has the player release an air-filled balloon towards a square wall. In the middle of the wall is a triangular target. What is the probability that the balloon will not hit the target?
Park 50 miles
Use the area formulas.
Simplify the powers. Subtract.
818 Saxon Algebra 1
3.5 ft.
4 ft.
7 ft.