Copyright(C) Ed2NetLearning.Inc1 PROBABILITY AND AREA

copyright(C) Ed2NetLearning.Inc 1

PROBABILITY AND AREA


PREVIOUS KNOWLEDGE• Write each fraction in simplest form:1. 8 16 2. 4 20 3. 16 644. 9 215. 27 81


OBJECTIVE

• To find probability using area models

• With a very large sample, the experimental probability is close to the theoretical probability. The probability can be expressed as the ratio of areas.


PROBABILITY AND AREA

• The probability of landing in a specific region of a target is the ratio of the area of the specific region to the area of the target.

• P (specific region) = area of specific region

area of the target


Example – Find Probability Using Area Models

Find the probability that a dart thrown randomly will land in the shaded region.

P (shaded region) = area of shaded region

area of target

= 8 = ½

16

So, the probability is ½, or 0.5 or 50%


NOW YOUR TURN

Find the probability that a dart thrown randomly will land in the shaded region.


Example- Use Probability To Make Predictions

• Christiana plans to throw her T-shirts into the stands using a sling shot. Find the probability that a T- shirt will land in the upper deck of the stands. Assume it is equally likely for a shirt to land anywhere in the stands.

22 ft

43 ft

360 ft

Upper deck

Lower deck

P (upper deck) = area of upper deck

area of the stands

Area of upper deck

L x w = 360 x 22 = 7,920 sq.ft

Area of stands

L x w = 360 x (22 + 43) = 360 x 65

= 23,400 sq.ft

P ( upper deck) = 7,920 ~ 1

23,400 3


More Examples• Predict how many times a T-shirt will land in the upper

deck of the stands if the cheerleaders throw 15 T – shirts.

• Let n = number of T-shirts landing in the upper deck.

n = 1

15 3

n x 3 = 15 x 1

3n = 15

n = 15 = 5

3

About 5, T- shirts will land in the upper deck.

T-shirts landing in the upper deck

T-shirts thrown


NOW YOUR TURN

• A game of throwing pebbles, what is the probability that the pebble will land in region B. assume it is equally likely for a pebble hit anywhere on the window.

A B C

D E F

30 in

30 in

18 in 18 in 18 in


Let’s solve this also• In the game of throwing pebbles into a region, predict

how many times a pebble will land in region B if we throw 300 pebbles.


REVIEW

• Find probability using area models

• With a very large sample, the experimental probability is close to the theoretical probability. The probability can be expressed as the ratio of areas.


ASSESSMENT• Find the probability that a randomly thrown dart will land in the

shaded region of each dartboard

5 ft

5 ft

3 ft

1

2

3


Assessment sheet

1 2 3

4 5 6

7 8 9

To win a prize, a dart must land on an even number. It is equally likely that the dart will land on anywhere of the dartboard.

4. What is the probability of winning a prize ?

5. Predict how many times a dart will land on an even number if it is thrown 9 times?

6. What is the probability of a randomly thrown dart landing on a consonant? 7. If 40 darts are randomly thrown, how many would predict to land on a consonant?

8. What is the probability of a randomly thrown dart landing on a vowel?

9. If200 darts are randomly thrown, how many would predict to land on a vowel?

10. Find the probability that a randomly thrown dart will land in the shaded region?

V Q W O

E Z I X


Great Job!

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Copyright(C) Ed2NetLearning.Inc1 PROBABILITY AND AREA