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Multiplication of Probability

Multiplication of Probability. Group 20. Group Members. Au Chun Kwok (98003350) Chan Lai Chun (98002770) Chan Wing Kwan (98002930) Chiu Wai Ming (98241940) Lam Po King (98003270). Before Use. This power point file is aiding for teaching Probability.

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Multiplication of Probability

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  1. Multiplication of Probability Group 20

  2. Group Members Au Chun Kwok (98003350) Chan Lai Chun (98002770) Chan Wing Kwan (98002930) Chiu Wai Ming (98241940) Lam Po King (98003270)

  3. Before Use This power point file is aiding for teaching Probability. We advise students using it under teacher’s instructions. It’s not necessary to use this package step by step, you can use in any order as you like. Hope you enjoy this package ! Hope you enjoy this package ! Hope you enjoy this package !

  4. Contents 1 Revision Some word from our group 3 Multiplication of Probability 2 Independent Events 4 Examples 6 Exercises 5 Summary

  5. Section 1: Revision Written by Chan Lai Chun (98002770) Lam Po King (98003270) Aid Recall the memory of definition probability Target To ensure each students has basic concept on probability

  6. Section 2: Independent Events Written by Chan Wing Kwan (98002930) Au Chun Kwok (98003350) Aid Define what an independent event is Show examples and non-examples of independent events Target Students can differentiate what an independent event is

  7. Section 3: Multiplication of Probability Written by Chan Lai Chun (98002770) Chiu Wai Ming (98241940) Aid Introduce the multiplication law of probability by stating definition; also provide examples and non-examples Target Students can distinguish a problem whether it can apply multiplication law Students can apply the multiplication law to the problem correctly

  8. Section 4: Examples Written by Chan Wing Kwan (98002930) Chiu Wai Ming (98241940) Aid To show what can we use the multiplication method in the problems of probability Target Try to show and do the examples with the students Show the connection between multiplication method and the probability that students learned before

  9. Section 5: Summary Written by Chiu Wai Ming (98241940) Lam Po King (98003270) Aid Revise and clarify some important concepts Target Help the students to consolidate the main ideas of this lesson

  10. Section 6: Exercises Written by Au Chun Kwok (98003350) Lam Po King (98003270) Aid Show some different types of example for the students Target Give a chance for the students to do some calculations on probability by applying multiplication law

  11. Contents 1 Revision Some word to say 3 Multiplication of Probability 2 Independent Events 4 Examples 6 Exercises 5 Summary

  12. 1. Revision I) Definition of Probability When all the possible outcomes of an event E are equally likely, the probability of the occurrence of E, often denoted by P(E), is defined as: I) Definition of Probability When all the possible outcomes of an event E are equally likely, the probability of the occurrence of E, often denoted by P(E), is defined as:

  13. 1. Revision I) Definition of Probability Example : The possible outcomes : ? =

  14. 1. Revision I) Definition of Probability Example : The possible outcomes : ? = 1 2 3 4 9 9 5 6 7 8

  15. 1. Revision I) Definition of Probability Example : The possible outcomes : 1 3 3 1 2 ? = 3 9

  16. Why ? 1. Revision II) P(E)=1the probability of an event that is certainto happen II) P(E)=1the probability of an event that is certain to happen Example : A coin is tossed. P(head or tail) = 1 Since the possible outcomes are $5 and and they are also favourable outcomes.

  17. Why ? 1. Revision III) P(E)=0the probability of an event that is certain NOT to happen III) P(E)=0the probability of an event that is certain NOT to happen Example : A die is thrown. P(getting a ‘7’) = 0 Since the possible outcomes are , , , , and impossible

  18. < < < < 1. Revision IV) 0 P(E) 1 0 1/2 1 evenly likely impossible certain unlikely likely

  19. Independent events 2. Independent Events Definition Two events are said to be independentof the happening of one event has no effect on the happening of the other.

  20. 2. Independent Events Example: 1. Throwing a die and a coin. Let A be the event that ‘1’ is being thrown. Let B be the event that ‘Tail’ is being thrown. Then A and B are independent events. 2. Choosing an apple and an egg. Let C be the event that a rotten apple is chosen. Let D be the event that a rotten egg is chosen. Then C and D are independent events.

  21. 2. Independent Events Non-example: 1. Throwing 2 dice. Let A be the event that any number is thrown. Let B be the event that a number which is greater than the first number is thrown. Since the second number is greater than the first number, B depends on A. Therefore, A and B are NOT independent.

  22. 2. Independent Events Non-example: 2. Choosing 2 fruits. Let C be the event that a banana is chosen first. Let D be the event that an apple is then chosen. Since a banana is chosen first and an apple is then chosen, D is affected by C. Therefore, C and D are NOT independent.

  23. 2. Independent Events Question 1 Throwing 2 dice. Let A be the event that ‘Odd’ is being thrown. Let B be the event that ‘divisible by 3’ is being thrown. Are A and B independent?

  24. Independent events 2. Independent Events Congratulation! Throwing 2 dice. Event A = the result is ‘Odd’. Event B = the result is ‘divisible by 3’. Event A and event B are independent because they do not affect each other.

  25. Independent events 2. Independent Events Sorry. The correct answer is... Throwing 2 dice. Event A = the result is ‘Odd’. Event B = the result is ‘divisible by 3’. Event A and event B are independent because they do not affect each other.

  26. 2. Independent Events Question 2 Catching 2 fishes. Let A be the event that the cat catches a golden fish first. Let B be the event that the cat then catches a fish which is NOT golden. Are A and B independent?

  27. 2. Independent Events Sorry. The correct answer is... Catching 2 fishes. Event A = the result is ‘Golden’. Event B = the result is ‘Not Golden’. After the first catching, the total number of outcomes and the number of favourable outcomes changes. That is, B depends on A; therefore, A and B are NOT independent.

  28. 2. Independent Events Congratulation! Catching 2 fishes. Event A = the result is ‘Golden’. Event B = the result is ‘Not Golden’. After the first catching, the total number of outcomes and the number of favourable outcomes changes. That is, B depends on A; therefore, A and B are NOT independent.

  29. 2. Independent Events Question 3 Throwing 1 die and 1 coin. Let A be the event that ‘Odd’ is being thrown. Let B be the event that ‘Head’ is being thrown. Are A and B independent?

  30. Independent events 2. Independent Events Congratulation! Throwing 1 die and 1 coin. Event A = the result is ‘Odd’. Event B = the result is ‘Head’. Event A and event B are independent because they do not affect each other.

  31. Independent events 2. Independent Events Sorry. The correct answer is... Throwing 1 die and 1 coin. Event A = the result is ‘Odd’. Event B = the result is ‘Head’. Event A and event B are independent because they do not affect each other.

  32. 3. Multiplication of Probability If there are 2 independent events A and B, we can calculate the probability of A and B by applying to Multiplication Law: P(A and B) = P(A) P(B)

  33. What is the number of possible outcomes of throwing a die? What is the number of possible outcomes of tossing a coin ? 3. Multiplication of Probability

  34. T H 3. Multiplication of Probability What is the number of possible outcomes of throwing a die? What is the number of possible outcomes of tossing a coin ?

  35. 3. Multiplication of Probability What is the total number of possible outcomes of throwing a die and tossing a coin at the same time? T H

  36. 3. Multiplication of Probability What is the total number of possible outcomes of throwing a die and tossing a coin at the same time? Total Possible Outcomes = 2  6 =12

  37. 3. Multiplication of Probability What is the probability of getting a headandan odd number? P(H and Odd)

  38. Try another one, OK!? GO... Try another one, OK!? GO... Try another one, OK!? GO... 3. Multiplication of Probability

  39. 3. Multiplication of Probability Find the probability that one die shows an ‘Odd’ number and the other die shows a number ‘divisible by 3’.

  40. 3. Multiplication of Probability Find the probability that one die shows an ‘Odd’ number and the other die shows a number ‘divisible by 3’. Solution: P(one oddandone divisible by 3) = P(one odd)  P(one divisible by 3)

  41. and P(A and B) = P(A)  P(B)  A and B are independent events. 3. Multiplication of Probability Condition!?

  42. Example 1 In a class, there are 9 students, they are John, Peter, Paul, Sam, Mary, Anna, Susan, Sandy and Betty. What is the probability of choosing Sam and Mary as the monitor and monitress?

  43. In a class, there are 9 students, they are John, Peter, Paul, Sam, Joe, Mary, Susan, Sandy and Betty. What is the probability of choosing Sam and Mary as the monitor and monitress? Total no. of boys = 4 Total no. of girls = 5 P( Sam ) = P( Mary ) = Thus the probability is = =

  44. Example 2 The probability of Peter to pass Chinese, English and Mathematics are 3/4, 4/5 and 1/3 respectively. Find the probability that he passes Chinese and Mathematics only? Chinese English Mathematics What is this?

  45. The probability of Peter to pass Chinese, English and Mathematics are 3/4, 4/5 and 1/3 respectively. Find the probability that he passes Chinese and Mathematics only? P(fail English) Thus the probability of Peter passes Chinese and Mathematics only is Peter pass Chinese and Mathematics only, that means…… English Fail What is this?

  46. Example 3 One letter is chosen at random from each of the words: SELECTED EFFECTIVE METHOD Find the probability that three letters are the same.

  47. Which letter should be choose : SELECTED EFFECTIVE EFFECTIVE METHOD METHOD METHOD SELECTED EFFECTIVE METHOD E probability that three letters are the same SELECTED, P(‘E’) = EFFECTIVE, P(‘E’) = METHOD, P(‘E’) =

  48. 5. Summary Definition of independent event: Two events are said to beindependentof the happening of one event has no effect on the happening of the other. independent no effect

  49. Multiplication Law Then, how can we write? P(A and B) = P(A)  P(B) and  Condition: where A and B are independent events independent events A and B are independent events

  50. Exercise 1 Euler goes to a restaurant to have a dinner. He can choose beef, pork or chicken as the main dish and the probability of each is 0.3, 0.2 and 0.5 respectively. He can choose rice, spaghetti or potato to serve with the main dish and the probability of each is 0.1, 0.6 and 0.3 respectively. Find the probability that he chooses beef with spaghetti.

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