1. Copyright©Ed2NetLearning.Inc 1 OUTCOMES

2. Copyright©Ed2NetLearning.Inc 2 Previous Knowledge 1. A number cube is rolled. What is the probability of rolling a composite number? Answer: 1/3 2. List all the outcomes for the following experiments> a. tossing a coin – head & tail b. rolling a number cube – 1, 2, 3, 4, 5, 6 c. choosing a color of the American flag - red, white, blue.

3. Copyright©Ed2NetLearning.Inc 3 OUTCOMES- OBJECTIVES 1. To understand sample space 2. To find the outcomes using lists and tree diagrams.

4. Copyright©Ed2NetLearning.Inc 4 SAMPLE SPACE - DEFINITION The set of all possible outcomes is called the sample space. Example: The sample space for rolling a cube is listed as { 1, 2, 3, 4, 5, 6} There are 6 possibilities. A tree diagram can also be used to show a sample space. A tree diagram is a diagram that shows all possible outcomes of an event.

5. Copyright©Ed2NetLearning.Inc 5 Sample Space QTake 2 dice and throw them together. The possible outcomes are: A{ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)} The set of all outcomes is a sample space. The above example is a sample space. There are 36 possibilities.

6. Copyright©Ed2NetLearning.Inc 6 Now your turn QTake 2 coins and toss them. Write the sample space? A { (H,H) (H,T) (T,H) (T,T)}

7. Copyright©Ed2NetLearning.Inc 7 FIND A SAMPLE SPACE Q.How many outfits are possible from a choice of blue or black shorts and a choice of yellow, orange or red shirt? A. Shorts ShirtOutcome blue(B) White(w) there are 6 possible outfits. Yellow (y) Orange (o) Red (r) Yellow(Y) Orange(o) Red (r ) BY BO BR WY WO WR

8. Copyright©Ed2NetLearning.Inc 8 Now your turn A car can be purchased with two doors and four doors. You can also choose leather, fabric or cushion seats. Draw a tree diagram. 2 doors (2) 4 doors(4) Leather(l) Fabric(f) Cushion(c ) Leather(L) Fabric(F) Cushion(C ) 2L 2F 2C 4L 4F 4C

9. Copyright©Ed2NetLearning.Inc 9 Find Probability When you know the number of outcomes, we can easily find the probability that an event can occur. Probability = Number of ways an event can happen Total number of possible outcomes

10. Copyright©Ed2NetLearning.Inc 10 Find probability Q. Two coins are thrown. What is the probability that both are heads? First write the sample space. (H,H) (H,T) (T,H) (T,T) There are 4 possibilities Probability of both showing head is (H,H) That is only 1 possibility Probability = ¼

11. Copyright©Ed2NetLearning.Inc 11 Now Your Turn Q. Two dice are thrown. i) What is the probability that both dice showing 1? ii) what is the probability that both showing the same number? A. i) Total number of outcomes = 36 Number of possible ways in which both dice showing 1 = 1 Probability = 1 36 ii) Total number of outcomes =36 Number of possibilities in which both dice showing the same number = 6 {(1,1) (2,2) (3,3) (4,4) (5,5) (6,6)} Probability = 6 36

12. Copyright©Ed2NetLearning.Inc 12 Use Tree Diagram To Find Probability Q. Max spins two spinners. What is the probability of spinning yellow on the first spinner and red on the second spinner? Spinner 1Spinner 2 R Y R Y Yellow(Y) Red(R) One outcome has yellow and then red. There are 4 possible outcomes. So P (yellow, red) = ¼ YELLOW(y) RED(r ) YELLOW (y) RED ( R ) YY YR RY RR

13. Copyright©Ed2NetLearning.Inc 13 Another example to find probability from a tree diagram Q. A penny is tossed and a number cube is rolled. Use a tree diagram to find the probability of getting a head and a 5. PennyNumber cubeOutcome 1 H1 Heads(H) 2 H2 3 H3 4 H4 5 H5 6 H6 Tails(T) 1 T1 2 T2 3 T3 4 T4 5 T5 6 T6 Total outcomes = 12 So, P(head,5) = 1 12

14. Copyright©Ed2NetLearning.Inc 14 Now Your Turn Chocolate, vanilla, strawberry icecreams with sugar or waffle cone. How many outcomes are possible? Find P (chocolate,sugar) ? chocolate vanilla strawberry There are 6 outcomes. P (chocolate,sugar) = 1/6 Sugar Waffle cone Sugar Waffle cone Sugar Waffle cone Chocolate,sugar Chocolate, waffle cone Vanilla sugar Vanilla waffle cone Strawberry sugar Strawberry waffle cone

15. Copyright©Ed2NetLearning.Inc 15 Review 1. To understand sample space 2. To find the outcomes using lists and tree diagrams. 3. To find the probability using tree diagram

16. Copyright©Ed2NetLearning.Inc 16 Assessment 1. From a group of 2 men and 3 women two persons are selected. Describe the sample space of the experiment. Let M 1, M 2, W 1, W 2, W 3 represents men and women in the group. sample space = { M 1 M 2, M 1 W 1, M 1 W 2, M 1 W 3, M 2 W 1, M 2 W 2, M 2 W 3, W 1 W 2, W 1 W 3, W 2 W 3 } 2. Two dice are thrown simultaneously. Find the probability of getting a multiple of 3 as the sum? 1 3

17. Copyright©Ed2NetLearning.Inc 17 Assessment 3. A bag contains 5 white, 7 black and 8 red balls. A ball is chosen at random. What is the probability that it is a red ball or a white ball? total number of balls = 5+7+8 = 20 P (ball is red or white) = 8 + 5 = 13 20 20 4. Three coins are tossed. Find the probability of getting atleast two heads? ½ 5. A coin is tossed. If it shows head, we draw a ball from a bag containing 3 red and 4 black balls. Write the sample space ? { HR 1, HR 2, HR 3, HB 1, HB 2, HB 3 and HB 4 }

18. Copyright©Ed2NetLearning.Inc 18 Assessment 6. In a single throw of 3 dice, find the probability of getting a total less than 5? Sample space = { (1,1,1),(1,1,2), ……,(6,6,6)} number of possible outcomes = 6 x 6 x 6 = 216 Possible outcomes = (1,1,1), (1,1,2) (1,2,1), (2,1,1) = 4 P (total less than 5) = 4 = 1 216 54 7. An urn contains 8 red, 3 white and 9 blue balls. If 1 balls is chosen at random. Determine the probability that the ball is red? 8 20

19. Copyright©Ed2NetLearning.Inc 19 Assessment 8. From a bag containing 5 red and 4 black balls, a ball is drawn at random. What is the probability that it is a black ball? 4 9 9. Find the probability of getting a ‘king’ or a ‘queen’ in a single draw from a well shuffled pack of playing cards? 2 13 10. A family has 2 boys and 3 girls. Two persons are selected. Write down the sample space of this experiment. { G 1 G 2,G 1 G 3,G 2 G 3, G 1 B 1, G 1 B 2, G 2 B 1, G 2 B 2, G 3 B 1, G 3 B 2, B 1 B 2 }

20. Copyright©Ed2NetLearning.Inc 20 Great Job!