1. copyright(C) Ed2NetLearning.Inc1 PROBABILITY AND AREA

2. copyright(C) Ed2NetLearning.Inc2 PREVIOUS KNOWLEDGE Write each fraction in simplest form: 1.8 16 2.4 20 3.16 64 4.9 21 5.27 81

3. copyright(C) Ed2NetLearning.Inc3 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.

4. copyright(C) Ed2NetLearning.Inc4 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

5. copyright(C) Ed2NetLearning.Inc5 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%

6. copyright(C) Ed2NetLearning.Inc6 NOW YOUR TURN Find the probability that a dart thrown randomly will land in the shaded region.

7. copyright(C) Ed2NetLearning.Inc7 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

8. copyright(C) Ed2NetLearning.Inc8 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

9. copyright(C) Ed2NetLearning.Inc9 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. AB C DEF 30 in 18 in

10. copyright(C) Ed2NetLearning.Inc10 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.

11. copyright(C) Ed2NetLearning.Inc11 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.

12. copyright(C) Ed2NetLearning.Inc12 ASSESSMENT Find the probability that a randomly thrown dart will land in the shaded region of each dartboard 5 ft 3 ft 1 2 3

13. copyright(C) Ed2NetLearning.Inc13 Assessment sheet 123 456 789 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? VQWO EZIX

14. copyright(C) Ed2NetLearning.Inc14 Great Job!