copyright(c) ed2netlearning.inc1 probability and area
TRANSCRIPT
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PREVIOUS KNOWLEDGE• Write each fraction in simplest form:1. 8 16 2. 4 20 3. 16 644. 9 215. 27 81
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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.
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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
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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%
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NOW YOUR TURN
Find the probability that a dart thrown randomly will land in the shaded region.
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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
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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
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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
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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.
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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.
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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
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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