Transcript Lesson 1 Contents

Transparency 11-5
5-Minute Check on Lesson 11-4
Find the area of each figure. Round to the nearest tenth if necessary.
14
1.
2.
A = 100.7 units²
10
3.
A = 330 units²
15
15
4.
12
8
3
8
A = 117.7 units²
A = 120 units²
8
5. Find the area
of the figure
14
A = 12 units²
6.
Standardized Test Practice:
A
112 units²
B
Find the figure’s area.
136.8 units²
C
162.3 units²
Click the mouse button or press the
Space Bar to display the answers.
D
212.5 units²
Lesson 11-5
Geometric Probability
Objectives
• Solve problems involving geometric
probability
• Solve problems involving sectors and
segments of circles
Vocabulary
• Geometric Probability – probability involving
geometric measure such as length or area
• Sector – of a circle is bounded by a central angle and
its intercepted arc
• Segment – region of a circle bounded by and arc and
a chord
Circles - Probability
Pie Charts
135°
180°
y
Probability
0 = no chance
1 = for sure
90°
135º
------ = 3/8
360º
or .375 or 37.5%
Center
180º
------ = 1/2
360º
or .5 or 50%
Radius (r)
45º
------ = 1/8
360º
or .125
or 12.5%
270°
Circumference = 2πr = dπ
315°
x
0°
Geometric Probability
Probability
Probability
Area of Event
-----------------Total Area
Area of Event
¼ * πr2
------------------ = --------Total Area
πr2
Event (e)
S
Center
0 ≤ P(e) ≤ 1
Radius (r)
T
¼ * πr2
P(e) = --------πr2
¼
= -------- = 0.25
1
Grid-In Test Item A game board consists of a circle inscribed in
a square. What is the chance that a dart thrown at the board will
land in the shaded area?
Read the Test Item
You want to find the probability of landing in the shaded area, not
the circle.
Solve the Test Item
We need to divide the area of the shaded region by the total area
of the game board.
The total area of the board is
square inches.
The area of the shaded region is the area of the total
board minus the area of the circle. The area of the circle
is
The probability of throwing a dart onto the shaded area is
or about 0.215.
Grid In Test Item A square game board consists of shaded and
non-shaded regions of equal width as shown. What is the
chance that a dart thrown at the board will land in a shaded
area?
Answer: 0.595
Find the area of the shaded sectors.
The shaded sectors have degree
measures of 45 and 35 or 80°
total. Use the formula to find the
total area of the shaded sectors.
Area of a
sector
Simplify.
Answer:
Area of the shaded sectors is 18π or about 56.5 sq inches.
Find the probability that a point chosen at random lies in the
shaded region.
To find the probability, divide the
area of the shaded sectors by the
area of the circle. The area of the
circle is πr² with a radius of 9.
Geometric probability formula
Simplify.
Use a calculator.
Answer:
The probability that a random point is in
the shaded sectors is or about 0.22.
Geometric probability formula
Simplify.
Use a calculator.
Answer:
The probability that a random point is in
the shaded sectors is or about 0.22.
a. Find the area of the orange sectors.
Answer:
or about
b. Find the probability that a
point chosen at random lies
in the orange region.
Answer:
or about 0.33
Summary & Homework
• Summary:
– To find geometric probability, divide the area of a
part of a figure by the total area
• Homework:
– pg 625-627; 10-15