1. Copyright©Ed2NetLearning.Inc1 REVIEW OF PROBABILITY

2. Copyright©Ed2NetLearning.Inc2 PREVIOUS KNOWLEDGE 1. Write 7 1. Write 7 in simplest form = 1 639 639 2. Write 5 x 3 2. Write 5 x 3 in simplest form = ¼ 6 10 3. Write 4 x 2 in simplest form = 8 7 3 21 4. Solve a = 5 a = 2 6 15 5. Solve 8 = 28 y = 12 y 42

3. Copyright©Ed2NetLearning.Inc3 THEORETICAL PROBABILITY

4. Copyright©Ed2NetLearning.Inc4 THEORETICAL PROBABILITY- DEFINITION The theoretical probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes.The theoretical probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes. P (event) =P (event) = number of favorable outcomes number of possible outcomes number of possible outcomes The probability that an event will occur is a number from 0 to 1.

5. Copyright©Ed2NetLearning.Inc5 Example – Find Probability In a spinner there are 8 equally likely outcomes – red, blue, green, yellow, orange, violet, white, black. Find the probability of spinning white.In a spinner there are 8 equally likely outcomes – red, blue, green, yellow, orange, violet, white, black. Find the probability of spinning white. P (white) =P (white) = number of favorable outcomes number of possible outcomes number of possible outcomes = 1 8

6. Copyright©Ed2NetLearning.Inc6 Now your turn A paper is cut into circular shapes and in that numbers from 1 – 10 is written. A number is taken at random. Find the probability that the number chosen is i) 1 and ii) primeA paper is cut into circular shapes and in that numbers from 1 – 10 is written. A number is taken at random. Find the probability that the number chosen is i) 1 and ii) prime P ( 1 ) = 1P ( 1 ) = 1 10 10 P ( prime ) = 2 5

7. Copyright©Ed2NetLearning.Inc7 Complementary Events Complementary events are two events in which either one or the other must happen, but they cannot happen at the same time. An example is a coin landing on heads or not landing on heads. The sum of the probabilities of complementary events is 1.Complementary events are two events in which either one or the other must happen, but they cannot happen at the same time. An example is a coin landing on heads or not landing on heads. The sum of the probabilities of complementary events is 1.

8. Copyright©Ed2NetLearning.Inc8 Use Probability To Solve a Problem In the television news hour it is reported that there is a 25% chance of raining. What is the probability that it will not rain?In the television news hour it is reported that there is a 25% chance of raining. What is the probability that it will not rain? P ( rain) + P ( not raining) = 1 P ( rain) + P ( not raining) = 1 0.25 + P ( not raining ) = 1 0.25 + P ( not raining ) = 1 P ( not raining ) = 1 – 0.25 = 0.75 P ( not raining ) = 1 – 0.25 = 0.75 = 75 = 75% = ¾ 100 100

9. Copyright©Ed2NetLearning.Inc9 Let’s try by yourself A sports magazine predicted that Super Kings had a 30% chance of winning Golf Championship. What is the probability that the Super Kings will not win?A sports magazine predicted that Super Kings had a 30% chance of winning Golf Championship. What is the probability that the Super Kings will not win? P ( win ) + P ( not winning) = 1P ( win ) + P ( not winning) = 1 0.3+P ( not winning) = 1 P ( not winning ) = 1 – 0.3 P ( not winning ) = 1 – 0.3 = 0.7 = 0.7

10. Copyright©Ed2NetLearning.Inc10 OUTCOMES

11. Copyright©Ed2NetLearning.Inc11 OUTCOMES The set of all possible outcomes is called the sample space. A tree diagram can also be used to show a sample space. When you make a tree diagram, you have an organized list of outcomes.The set of all possible outcomes is called the sample space. A tree diagram can also be used to show a sample space. When you make a tree diagram, you have an organized list of outcomes. A tree diagram is a diagram that shows all possible outcomes of an event.A tree diagram is a diagram that shows all possible outcomes of an event.

12. Copyright©Ed2NetLearning.Inc12 Use a tree diagram to find probability A car can be purchased with black or white. You may also choose leather, fabric or vinyl seats. Draw a tree diagram that shows all the buying options. What are the possible outcomes?A car can be purchased with black or white. You may also choose leather, fabric or vinyl seats. Draw a tree diagram that shows all the buying options. What are the possible outcomes? Car colorSeatsOutcomes Black White Leather (L) Fabric (F) Vinyl (V) BL BF BV Leather (L) Fabric (F) Vinyl (V) WL WF WV The possible outcomes are 6

13. Copyright©Ed2NetLearning.Inc13 NOW YOUR TURN There are 2 spinners. In the 1 st one, 2 colors – pink and grey are there and in the 2 nd one, X, Y, and Z are marked. Draw s tree diagram to show the sample space for the situation. How many outcomes are possible? Find P ( pink, Y) ?There are 2 spinners. In the 1 st one, 2 colors – pink and grey are there and in the 2 nd one, X, Y, and Z are marked. Draw s tree diagram to show the sample space for the situation. How many outcomes are possible? Find P ( pink, Y) ? spinner 1spinner 2 outcomes Pink Grey XYZXYZ XYZXYZ PX PY PZ GX GY GZ There are 6 possible outcomes. P ( PY) = 1/6

14. Copyright©Ed2NetLearning.Inc14 MAKING PREDICTIONS ABOUT PROBABILITY

15. Copyright©Ed2NetLearning.Inc15 What is Survey and Population A survey is a method of collecting information. The group being studied is the population. Sometimes, the population is very large. Part of the group called a sample is surveyed.A survey is a method of collecting information. The group being studied is the population. Sometimes, the population is very large. Part of the group called a sample is surveyed. A good sample isA good sample is  selected at random or without preference,  representative of the population, and  large enough to provide accurate data.

16. Copyright©Ed2NetLearning.Inc16 Determine a Good Sample Every ninth person entering into a market is asked to state whether his or her favorite clothing shop. Determine whether the sample is a good sample.Every ninth person entering into a market is asked to state whether his or her favorite clothing shop. Determine whether the sample is a good sample. The sample is good because asking every 9 th person ensures a random survey, the sample is large enough to provide accurate information.The sample is good because asking every 9 th person ensures a random survey, the sample is large enough to provide accurate information.

17. Copyright©Ed2NetLearning.Inc17 Exercise Every 4 th person entering into a public road is asked whether he or she owns a pet. Determine whether the sample is a good sample.Every 4 th person entering into a public road is asked whether he or she owns a pet. Determine whether the sample is a good sample. The sample is a good one, since it is large enough, random, and represents the community ( a larger population)The sample is a good one, since it is large enough, random, and represents the community ( a larger population)

18. Copyright©Ed2NetLearning.Inc18 Let’s take a break!

19. Copyright©Ed2NetLearning.Inc19

20. Copyright©Ed2NetLearning.Inc20 Make predictions using proportions Use the information in the table, what is the probability that a student at the school ride a bike to school. P ( ride bike) = number of students that ride a bike number of students surveyed P ( ride bike) = 10 = ¼ 40 Q. There are 400 students at the school. Predict how many students would prefer bike to school. ¼ = s 400 1 x 400 = 4s s =400 = 100 4 100 students prefer bike to school. School Transportation MethodStudents Walk10 Ride bike 10 Ride bus 15 Get ride 5

21. Copyright©Ed2NetLearning.Inc21 NOW YOUR TURN A random sample of 40 flower shop customers was surveyed to find customer’s favorite flowers. The table shows the results. The shop expects to sell 50 bunches of flowers. How many bunches of each flower should the shop orderA random sample of 40 flower shop customers was surveyed to find customer’s favorite flowers. The table shows the results. The shop expects to sell 50 bunches of flowers. How many bunches of each flower should the shop order Type shoppersType shoppers daisy8 sunflower 4 rose20 mum8 Answer Daisy10 bunches Sunflower 5 bunches rose25 bunches mum10 bunches.

22. Copyright©Ed2NetLearning.Inc22 PROBABILITY AND AREA

23. Copyright©Ed2NetLearning.Inc23 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.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 regionP (specific region) = area of specific region area of target

24. Copyright©Ed2NetLearning.Inc24 Probability & Area Area of the whole region = l x w = 3 x 4 = 12Area of the whole region = l x w = 3 x 4 = 12 Area of the shaded region = 3 x 1 = 3 P ( specific region) = 3 = 1/4P ( specific region) = 3 = 1/412 Find the probability that a randomly thrown dart will land in the shaded region of each dartboard.Find the probability that a randomly thrown dart will land in the shaded region of each dartboard. If the dart is thrown 40 times, how many times would you expect to land it on the shaded region? ¼ = n/40 4n = 40 ; n = 40 = 10. So 10 times it will land on the shaded region. 4

25. Copyright©Ed2NetLearning.Inc25 Now your turn Find the probability that a randomly thrown dart will land in the shaded region of each dartboard.Find the probability that a randomly thrown dart will land in the shaded region of each dartboard. 3in 3 in 5 in Area of the whole region = 5 x 5 = 25 in 2 Area of the non –shaded region = 3 x 3 = 9 in 2 Area of the shaded region = 25 -9 = 16 P (specific region ) = 16 25

26. Copyright©Ed2NetLearning.Inc26 Let’s solve Suppose you threw a dart 200 times at the dartboard shown here. How many times would you expect it to land in the shaded regionSuppose you threw a dart 200 times at the dartboard shown here. How many times would you expect it to land in the shaded region 3in 3 in 5 in P (specific region) = 16/25 16 = n 25 200 16 x 200 = 25 x n n = 16 x 200 25 = 128.

27. Copyright©Ed2NetLearning.Inc27 Probability of Independent Events Two or more events in which the outcome of one event does not affect the outcome of the other event are independent events.Two or more events in which the outcome of one event does not affect the outcome of the other event are independent events.  The outcome of rolling a number cube does not affect the outcome of choosing a marble from a bag. The probability of two independent events is found by multiplying the probability of the first event by the probability of the second event.The probability of two independent events is found by multiplying the probability of the first event by the probability of the second event.

28. Copyright©Ed2NetLearning.Inc28 Probability of Independent Events Example: A coin is tossed, and the spinner shown is spun. Find the probability of tossing heads and spinning a 3.Example: A coin is tossed, and the spinner shown is spun. Find the probability of tossing heads and spinning a 3.  P(heads) = ½P(3)=1/4  P(heads and 3) = ½ x ¼ or 1/8  So, the probability is 1/8, 0.125 or 12.5%

29. Copyright©Ed2NetLearning.Inc29 Your Turn! P(tails and even)P(tails and even)

30. Copyright©Ed2NetLearning.Inc30 Assessment sheet Alphonse asked every 4 th sixth grade student who walked into a school dance to name their favorite sport. football – 52; soccer – 22; baseball – 16; hockey - 10 1.Find the probability a student prefers football? 13/25 2.If there are 375 students in the 6 th grade, how many can be expected to prefer football? About 195 3. Find the probability that a randomly thrown dart will land in the shaded region of the dartboard. 3 mm 10 mm 14 mm Answer: 4 5

31. Copyright©Ed2NetLearning.Inc31 Assessment Sheet 4. Suppose 60% of kids like video games. Predict the number of kids that prefer video game out of a group of 200 kids? 120 5. How many different jeans and shirt combinations can be made with blue jeans and black jeans, and a white shirt, a blue shirt and a yellow shirt? 6 6. The probability of a die landing on 6 is 1/6. The 1 in the numerator stands for the number of ways that a die lands on 6. what does 6 stands for? Number of possible outcomes.

32. Copyright©Ed2NetLearning.Inc32 Assessment Sheet 7.If a dart is thrown at the dartboard shown, what is the probability that it will hit the region C? 4/9 8.What is the probability that a dart will land within the large square but outside the small square? 8/9 9.The probability that it will rain on Saturday is 65%. The probability that it will rain on Sunday is 40%. What is the probability that it will rain on both days? 26% 10.Out of 50 students, 14 are interested in publishing a school news paper. What is the probability that a student at this school would be interested in publishing a school news paper? 7/25 BBC CBC ABC 12 CM 12 CM 4cm

33. Copyright©Ed2NetLearning.Inc33 Review The theoretical probability of an event is a ratio that compares the number of favorable outcomes to the number of possible outcomes. P (event) = number of favorable outcomes number of possible outcomes The set of all possible outcomes is called the sample space. A tree diagram can also be used to show a sample space. When you make a tree diagram, you have an organized list of outcomes. A survey is a method of collecting information. The group being studied is the population. Sometimes, the population is very large. Part of the group called a sample is surveyed. A good sample is   selected at random or without preference,   representative of the population, and   large enough to provide accurate data. 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.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.

34. Copyright©Ed2NetLearning.Inc34 That’s the end of this lesson. Try to do the assessment sheet We will meet you soon