Likelihood
Certain
Probability as a
Fraction
8/8 = 1/1 = 1
Probability as a
Decimal
Probability as a %
1.0 = 1 100/100 = 100%
No Chance 0/8 = 0
Good Chance 6/8 = 3/4
0.0 = 0
0.75
0/100 = 0%
75/100 = 75%

This lesson will use two basic principles.
The first principle involves the lengths of segments.
Suppose a point P of XY is picked at random .
Then: probability that P is on XQ
 length of XQ length of XY
X
Q
Y

13 spaces
6 spaces
4 spaces
1) A point X is picked at random on AF a.
.
What is the probability that X is on:
AC
4/13 b.
CD
2/13
A B c. d.
DF
6/13 7/13
C D
2 spaces
E
7 spaces e.
AG
It is certain.
1
15 spaces
F G
2 spaces
(not between A and F) f.
FG
0

2. M is the midpoint of JK , Q is the midpoint of MK , and X is the midpoint of MQ
.
J M X Q
½
K
.

3) Every 20 minutes a bus pulls up outside a busy department store and waits for five minutes while passengers get on and off. Then the bus leaves. If a person walks out of the department store at a random time, what is the probability that a bus is there?
Think of it as a timeline!
5 minutes/20 minutes
The probability that a bus is there is ¼ .
One Full Cycle
0 min.
5 min.
20 min.
Bus Arrives Bus Departs

4) A piece of rope 20 ft long is cut into two pieces at a random point.
What is the probability that both pieces of rope will be at least 3 ft long?
14/20 = 7/10
14 feet of rope to cut!
3 feet
Do not cut or one piece will be less than 3 feet!
20 feet
3 feet
Do not cut!
The probability of cutting the rope so both pieces will be at least 3 feet is 70%.

The second principle of geometric probability involves areas of regions.
Suppose a point P of region A is picked at random. Then:
A
A probability that P is in region B =
area of region B area of region A

If a value of pi is required in the following exercises, use π
= 3.14.
5. A dart lands at a random point on the square dartboard shown. a) What is the probability that the dart lands within the larger circle?
Probability =
Area of larger circle
Area of square
=
3.14(10) 2
25 2
=
314
625
= 0.5024 = 50.24%
5 5
10
10
25 b) What is the probability that the dart lands within the smaller circle?
Probability =
Area of smaller circle
Area of square
=
3.14(5) 2
25 2
=
78.5
625
= 0.1256 = 12.56%

6. A circular archery target has diameter 60 cm. Its bull’s eye has diameter 10 cm.
a) If an amateur shoots an arrow and the arrow hits a random point on the target, what is the probability that the arrow hits the bull’s eye?
Probability =
Area of bull’s eye
Area of target
=
3.14(5) 2
3.14(30) 2
=
78.5
2826
= .0278
= 2.78%
5
30 b) After many shots, 100 arrows have hit the target. Estimate the number hitting the bull’s eye.
Using the answer of about 3% from above, approximately 3 of 100 would hit the target.

7. A dart is thrown at a board 200 cm long and 157 cm wide. Attached to the board are 10 balloons, each with radius 12 cm. Assuming that each balloon lies entirely on the board, what is the probability that a dart that hits the board also hits a balloon.
12
12
12
12
12 12
157
12
12
12
12
200
Probability =
10(Area of one balloon)
Area of board
=
10(3.14)(12) 2
200(157)
=
4521.6
31400
= 0.144
= 14.4%

8. A ship has sunk in the ocean in a square region 5 miles on a side. A salvage vessel anchors at a random spot in this square. Divers search half a mile in all directions from the point on the ocean floor directly below the vessel.
a) What is the approximate probability that they locate the sunken ship at the first place they anchor? 5 miles
½
Probability =
Search Area
Total Area
=
3.14( ½ ) 2
(5) 2
=
0.785
25
= .0314
= 3.14%
5 miles b) What is the approximate probability that they locate the sunken ship in five tries?
(Assume that the tries do not overlap.)
Multiply the last answer by 5 to get 15.7%

pg. 462 CE #1-4
WE #1-8