Geometric

1
Section 7-8

• Geometric
• Probability

2
Probability of an Event

• The probability of an event is the ratio of the
  number of favorable outcomes to the number of
  possible outcomes
• P(event) favorable outcomes
  possible outcomes

3
Geometric Probability

• Let points represent outcomes.

4
Example
1
2
4
5
6
7
3
What is the probability of a choosing a point
between points 4 and 6?
P (between 4 and 6) Length of favorable
segment
Length of entire segment
P (between 4 and 6) 2 1 or 25.
8 4
5
Example Time

• At the crosswalk the WALK light runs for 20
  seconds. The DONT WALK light runs for 30
  seconds.
• What is the probability that when you step to the
  curb the WALK sign is running?
• P(WALK) 20 2 40 50
  5
• P(DONT WALK) 30 3 60
  50 5

6
Example Area

• Find the probability a point lands in the yellow
  region.
• P(yellow) .5(6)(6) 18 3 30
  (10)(6) 60 10

10
6
7
Finding Probability using Area
Assume the radii of the concentric circles are
1,2,3, etc.
12 in
12 in

• P(Inner red) ?(1)² ?
  12² 144

8
Carnival Coin Toss

• To win a prize in a carnival game, you must toss
  a quarter so that it lands entirely within the
  circle shown below. Find the probability of this
  happening on one toss. Assume that the center of
  a tossed quarter is equally likely to land at any
  point with the 8 inch square.
• Radius of Circle 1 inch
• Radius of Quarter 15/32 inches .46875 in
• 1 in - .46875 in .53125 in ( or 17/32 inches)

8 in
r 1 in
The favorable area to land the quarter is
within the dotted line area
8 in
P(quarter landing in circle) area of dashed
circle
area of square
P(Quarter) ? (.53125)² 0.014 ? 1.4
8²
Quarter
r .53125 in
r .46875 in
9
Assignment

• Page 404
• 1-5, 8-20even, 21, 23-25, 40, 47