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Warm-Up Geometric Probability

Lesson Goals

Describe geometric

using

the words certain, likely,unlikely, and impossible.

Calculate geometric probabilityas a number between

and one.

? Lesson Question

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

random definite aim, reason, or pattern

area the size of a

geometric probability the of favorable outcomes to total possible

outcomes as it pertains to geometric figures

ratio an expression that two or more numbers

WK2

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Geometric ProbabilityWarm-Up

Area

Area is the measure of the of a surface.

A = . 4= cm2

The area of the parallelogram will be the

as the area of the rectangle.

h

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Geometric Probability

Slide

Defining Geometric Probability

Geometric probability describes the likelihood that a point chosen at random in a region will

be located in a part of that region.

The geometric probability that a randomly chosen point in the larger square is inside the shaded

square is the ratio of the area of the

region to the area of the square.

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Describing Likelihood

How likely is it that a coin tossed at random into each rectangle will land in the shaded region?

Likely Impossible

≈ 20%≈ 75%100%

Instruction

A B

CD X

Y Z

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Geometric Probability

Slide

4 Likelihood in the Real World

What is the likelihood of scoring 50 points when a ball lands in a random part of the scoring area – impossible, unlikely, likely, or certain?

The probability that the ball will land in the

50-point hole is to the

size of the entire scoring area.

It is going to be that you would score 50 points.

Finding a Geometric Probability

To find a geometric probability:

1. Find the area of the region representing the outcome.

2. Find the area of the figure.

3. Write the of those areas.

7

Instruction

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Geometric Probability

Calculating Geometric Probability on a Grid

This figure is made up of equally sized squares. What is the probability that a point randomly chosen on the grid will be in the shaded region?

• Find the area of the region representing

the outcome. 9

• Find the total area of the figure.

• Write the ratio of those areas.

7Slide

Instruction

P(shaded) = number of squares

number of squares

= 916

The figure shown is made up of equally sized squares. What is the probability that a point randomly chosen on the grid will be in the unshaded region?

• P(shaded) = 9

16

• P(unshaded) = − P(shaded) 9

16= 1 −

=

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Geometric Probability

Calculating Geometric Probability

What is the probability that a point chosen at random in the large square is in the shaded region?

Slide

9

Instruction

5 in.

2 in.

2 in.P(shaded) =

area of

area of large

area of triangle: 1

2bh =

1

2(2)(2) =

area of large square: s2 = (5)2 = 25

P (shaded) = 225 =

Find the probability that a point randomly chosen on the target will be in the middle ring.

Find the area of the middle ring:

Areas of the circles:small: 12.56 in.2

medium: 78.5 in.2

large: 200.96 in.2

  78.50−12.56

65.94≈ 0.328 ≈ %

Find the probability:

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Summary Geometric Probability

Lesson Question How do you find geometric probabilities?

Answer

?

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