1
Lesson # 11.7. Geometric Probability
Objective: Use lengths and areas to find geometric probabilities.
Homework: Study # 11.7; Handouts on # 11.7;
Probability and Length
Let AB be a segment that contains the segment CD . If a point K on AB
is chosen at random, then the probability that it is on CD is the ratio
of the length of CD to the length of AB .
P(K is on CD ) = ________
Example 1. Find the probability that a point chosen at random on
FJ is on GK .
Example 2. Shuttle. A shuttle to town runs every 10 minutes. The
ride from your boarding location to town takes 13 minutes. One
afternoon, you arrive at the boarding location at 2:41. You want to
get to town by 2:57. What is the probability you will get there by
2:57?
2
Probability and Area
Let J be a region that contains region M. If a point K in J is chosen at
random, then the probability that it is in region M is the ratio of the
area of M to the area of J.
P(K is in region M) = ________
Example 3.
Golf. A golf ball is hit and stops on the green. A prize is won if it stops
in the painted circle. The diameters of the green and circle are shown
at the right. If the ball is equally likely to stop on any point on the
green, what is the probability that a prize is won?
Example 4. Property. A homeowner’s property is shown in the
scale drawing. If a deer is equally likely to be anywhere on the
property, estimate the probability that it is on grass.