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# Probability

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### Probability

1. 1. CHAPTER 7 PROBABILITY ILydia TwinNor IzzatiNashasha NabilaSaidatuna MiftahulJannah
2. 2. Subtopic7.1 Concept of sample space7.2 Concept of events7.3 Use the concept of probability of an event to solve problems
3. 3. 7.1 The Concept Of Sample SpaceLearning Outcomes:• Determine whether an outcome is a possible outcome of an experiment• List all the possible outcomes of an experiment – From activities; – By reasoning• Determine the sample space of an experiment• Write the sample space by using set notation
4. 4. Learning outcome 1a) Determine whether an outcome is a possible outcome of an experimentExample 1:Determine whether the following are thepossible outcome when tossing a 10 sen and 50sen coin Case 1: Tossing a 10 sen coin I) A symbol of 10 sen II) A picture of a wau III) A symbol of 50 sen IV) A picture of congkak
5. 5. Cont…Case 2: Tossing a 50 sen coinI) A symbol of 20 senII) A picture of a wauIII) A picture of congkakIV) A symbol of 50 sen
6. 6. TRY THIS:A pouch contains orange, green, yellow andwhite coloured chips. If a chip is taken out atrandom, determine whether the followingoutcomes are possible.a) Getting a red chipb) Getting a green chipc) Getting a orange chipd) Getting a blue chipe) Getting a yellow chip
7. 7. Learning outcome 2b) Determine the possible outcomes of an experiment  From activities  By reason Example 2: A card is drawn from a set of cards written the letters R,E,S,P,E,C and T. Write down all the possible outcomes by reasoning. R E S P E C T
8. 8. ACTIVITY!!• Take out a coloured love paper from a small box that containing 3 red, 4 blue and 2 green love papers. – Use Tree Diagram, write down all the possible outcomes if 2 coloured love papers are taken out randomly.
9. 9. Learning outcome 3c) Determine the sample space of an experiment and write it by set notation Set of possible outcomes, S={ } Sample Space, S={ }Example 3: State the sample space by using set notation wheni) a dice is rolled.ii) Two die are rollediii) Two cards are picked randomly, one at the time, from three cards labelled with 1,2 and 3. Write the possible outcomes if:- 1. Without returning the first card. 2. Returning the first card after it is drawn
10. 10. Solutions to Examples
11. 11. Example 1Question: AnswerCase 1: Tossing a 10 sen Possible outcomesI) A symbol of 10 sen I) Possible --> II) Not PossibleII) A picture of a wau --> III) Not PossibleIII) A symbol of 50 sen -- IV) Possible >IV) A picture of congkak -->
12. 12. Example 1Question: AnswerCase 2: Tossing a 50 sen Possible outcomesI) A symbol of 20 sen I) Not Possible --> II) PossibleII) A picture of a wau --> III) Not PossibleIII) A picture of congkak --> IV) PossibleIV) A symbol of 50 sen -- >
13. 13. TRY THIS:A pouch contains orange, green, yellow andwhite coloured chips. If a chip is taken out atrandom, determine whether the followingoutcomes are possible.a) Getting a red chip  Not Possibleb) Getting a green chip  Possiblec) Getting a orange chip  Possibled) Getting a blue chip  Not Possiblee) Getting a yellow chip  Possible
14. 14. Example 2Question: A card is drawn from a set of cards written the letters R,E,S,P,E,C and T. Write down all the possible outcomes by reasoning. R E S P E C TAnswer:Possible outcomes: R, E, S, P, C, TWhy? Since we have 2 cards of letter E, we just take one of them.
15. 15. Example 3Answer:i) A dice is rolledS= {1, 2, 3, 4, 5, 6}ii) Two die are rolledS={(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)}iii) 1. Without returning the first card S={(1,2),(1,3),(2,1),(2,3),(3,1),(3,2)} 2. Returning the first card after it is drawn S={(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}
16. 16. Is one or more outcomes of theexperiment that satisfy certain conditions. A subset of the sample space
17. 17. 7.2a Identify the elements of a sample space which satisfy given conditions EXAMPLE: A box has 6 yellow marbles and 4 green marbles. If two marbles are picked, write down the elements of sample space
18. 18. SOLUTIONS = { GY , YG}Where, G – green Y – yellow
19. 19. 7.2b Elements of a sample space which satisfycertain conditions using set notation Example: Given element of sample space, S = (1,1) , (2,2) , (3,3) Written using set notation, P = { (1,1) , (2,2) , (3,3) } P is a subset of S
20. 20. 7.2c Determine whether an event ispossible for a sample space I) Event P is the event of getting number 4 = possible ii) Event Q is the event of getting blue card of number 3 = impossible iii) Event R is the event of getting yellow card of number 1 = possible
21. 21. Mathematics is FUN!=)
22. 22. Find the ratio of the number of times an event occurs to the numbers of trials.Probability of an event A is :  P(A)=Number of times event A occur Numbers of trial
23. 23. Therefore, for all the event, 0≤P(A)≥1
24. 24. 7.3b. Find the probability of an event from a big enough numbers of trials. solve By using the given formula in above, this questions. Type of softball Swimmin Badminto Squash game g n Number 550 250 350 150 of student Find the probability that the selected student likes. a) Softball b) badminton TRY IT !! =)
25. 25. SOLUTIONS,,,,, a)P(selected student likes softball)b) P(selected student like badminton)
26. 26. 7.3c. Find expected number of times an event willoccur, given the probability of the event and numberof trials At previous section, you have know that the probability of the event A Is: P(A)= Number of times event A occur Number of trials So, if we are given the probability of the event and the number of trials, we can find the number of times an event will occur which is: Number of times an event A occur = P(A)X Number of trials.
27. 27. TRY THIS….The probability to get red marble in a box is 0,8.If there is 200 marble inside the box,What is the number of red marble .Number of redmarble= P(A) x number ofmarble=0.8 x200=160 Help me solve this problem…..
28. 28. 7.3d Solve problems involving probability  Probability also being apply in real life problem. You can use the previous learning to solve the problem.
29. 29. TRY THIS PROBLEM…  of school transport by A survey is made on the mean student in SMK Jasa Murni.The data obtained is shown in the table below. Means of School bus bicycle Other means transport Number of 700 200 200 student If a student from a school is randomly picked, what is the probability that the student goes to school by: a) School bus b) Bicycle c) Other mean of transport.
30. 30. SoLuTiOns:  Total student= 700 +200 +200 =1100a)P(By school bus)=700/1100=7/11 b)P(by bicycle)=0.64 =200/1100 =2/11 c)P(by others ) =0.18 =200/1100 =2/11 =0.18
31. 31. END …Good luck everyone