1. Multiplication of Probability
Group 20

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

3. Before Use Hope you enjoy this package ! Hope you enjoy this package !
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 4 Examples 6 Exercises 5 Summary 2 Independent
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 ( )
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 ( )
Au Chun Kwok ( )
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 ( )
Chiu Wai Ming ( )
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 ( )
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 ( )
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 ( )
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 4 Examples 6 Exercises 5 Summary 2 Independent
Some word to say 3
Multiplication of
Probability 2
Independent
Events 4
Examples 6
Exercises 5
Summary

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

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

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

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

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

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

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. 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. 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. 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. 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. 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 ?

34. 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 ? T H

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 head and an odd number?
P(H and Odd)

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

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 odd and one divisible by 3)
= P(one odd)  P(one divisible by 3)

41. 3. Multiplication of Probability
P(A and B)
= P(A)  P(B) 
and
A and B are
independent events.
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……
Fail
English
What is this?

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

47. E SELECTED SELECTED EFFECTIVE EFFECTIVE EFFECTIVE METHOD METHOD METHOD
Which letter should be choose :
SELECTED
SELECTED
EFFECTIVE
EFFECTIVE
EFFECTIVE
METHOD
METHOD
METHOD
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 be independent of the happening of
one event has no effect on the happening of the other.
independent
no effect

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

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.

51. Exercise 1- Solution
Yeah! Finish!
Let’s try example 2.

52. Exercise 2 My old alarm clock
has a probability of 2/3 that it will go off.
If it doesn’t, there is still a probability of 3/4 that I’ll wake up
anyway in time to catch the 8 o’clock bus.
Even if it does go off, there is a probability of
1/6 that I’ll sleep through it and not get to the bus stop in time.
Find the probability that:
(a) I get to work
(b) I do not get to the bus stop in time.

53. Exercise 2 - Solution

54. Exercise 2 - Solution

55. Exercise 3 In a football match, team A has a penalty kick.
The coach is deciding which player to take that place.
It is known that the goalkeeper will defend the left, the central
and the right parts with probabilities of 0.3, 0.2 and 0.5
respectively.
(a) Find the probability that Beckham has
a goal if the probability of kicking the ball
to the left, central and right part is 0.6, 0.1
and 0.3.

56. Exercise 3 - Solution (a) P(Beckham has a goal)
= 1- P(left of goalkeeper) x P(right of player)
- P(central of goalkeeper) x P(central of player)
- P(right of goalkeeper) x P(left of player)

57. Exercise 3 In a football match, team A has a penalty kick.
The coach is deciding which player to take that place.
It is known that the goalkeeper will defend the left, the central
and the right parts with probabilities of 0.3, 0.2 and 0.5
respectively.
(b) Find the probability that
Owen has a goal if the probability
of kicking the ball to the left, central
and right part is 0.2, 0.5 and 0.3.

58. Exercise 3 - Solution

59. Exercise 3 In a football match, team A has a penalty kick.
The coach is deciding which player to take that place.
It is known that the goalkeeper will defend the left, the central
and the right parts with probabilities of 0.3, 0.2 and 0.5
respectively.
(c) Which player do you
think the coach
should choose?

60. Exercise 3
Ha ha…
Coach should choose me (Owen) because my probability of having a goal is greater than yours.

61. Some interest web page related to probability:
1. A game flipping a number of coins
2. A game opening one of the three doors

62. Thank you and Good bye