BAHAN AJAR MODUL pp_probab.ppt

MATH

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

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

5. Written byChan Lai Chun (98002770)
Lam Po King (98003270)
Section 1: Revision
AidRecall the memory of definition probability
TargetTo ensure each students has basic concept on probability

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

7. Written by Chan Lai Chun(98002770)
Chiu Wai Ming (98241940)
Section 3: Multiplication of Probability
AidIntroduce 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. Written byChan Wing Kwan(98002930)
Chiu Wai Ming (98241940)
Section 4: Examples
AidTo 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. Written byChiu Wai Ming (98241940)
Lam Po King (98003270)
Section 5: Summary
AidRevise and clarify some important concepts
TargetHelp the students to consolidate the main ideas of this
lesson

10. Written byAu Chun Kwok (98003350)
Lam Po King (98003270)
Section 6: Exercises
AidShow 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
4
Examples
1
Revision
3
Multiplication
of
Probability
2
Independent
Events
5
Summary
6
Exercises
Some word to say

12. outcomes possible
ofNumber
outcomes favourable
ofNumber
) E P( 
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. outcomes possible
ofNumber
outcomes favourable
ofNumber
) E P( 
1. Revision
I) Definition of Probability
Example : The possible outcomes :
?
=

14. 1. Revision
I) Definition of Probability
Example : The possible outcomes :

outcomes favourable
ofNumber
) E P( 
?
=
9
5
2
76
3
8
1
9
4

15. ) E P( 
1. Revision
I) Definition of Probability
Example : The possible outcomes :
?
=
9
3123
3
1
1
3

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

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

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

19. Definition Two events are said to be
independent of the happening
of one event has no effect
on the happening of the other.
2. Independent Events
I
n
d
e
p
e
n
d
e
n
t
e
v
e
n
t
s

20. 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. 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.
Example:

21. 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.
Non-example:
2. Independent Events
Since the second number is greater than the first number,
B depends on A.
Therefore, A and B are NOT independent.

22. 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.
Non-example:
2. Independent Events
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. 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.
2. Independent Events
Question 1
Are A and B independent?

24. 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.
I
n
d
e
p
e
n
d
e
n
t
e
v
e
n
t
s
2. Independent Events
Congratulation!

25. 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.
I
n
d
e
p
e
n
d
e
n
t
e
v
e
n
t
s
2. Independent Events
Sorry. The correct answer is...

26. 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.
2. Independent Events
Question 2
Are A and B independent?

27. 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 d
epends on A; therefore, A and B are NOT independent.
2. Independent Events
Sorry. The correct answer is...

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 d
epends on A; therefore, A and B are NOT independent.

29. 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.
2. Independent Events
Question 3
Are A and B independent?

30. 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.
I
n
d
e
p
e
n
d
e
n
t
e
v
e
n
t
s
2. Independent Events
Congratulation!

31. 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.
I
n
d
e
p
e
n
d
e
n
t
e
v
e
n
t
s
2. Independent Events
Sorry. The correct answer is...

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

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
TH
TH
TH
TH
TH
TH
= 2  6
=12

37. 3. Multiplication of Probability
What is the probability of getting a head and an odd number?
4
1

TH
TH
TH
TH
TH
TH
12
3

P(H and Odd)
Outcomes Possible Total
Outcomes Favourable










62
31

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
66
23



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)
6
2
6
3


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

42. 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?
Example 1

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?
4
1
Total no. of boys = 4 Total no. of girls = 5
P( Sam ) = P( Mary ) =
Thus the probability is =
5
1
5
1
4
1

20
1
=

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


234789
456123
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?
Peter pass Chinese and Mathematics only, that means……
P(fail English) Thus the probability of
Peter passes Chinese
and Mathematics only
is
5
1
5
4
1


20
1
3
1
5
1
4
3


English
What is this?

46. Example 3
One letter is chosen at random from each of the words:
SELECTEDSELECTED EFFECTIVEEFFECTIVE METHODMETHOD
Find the probability that three letters are the same.

47. Which letter should be
choose :
SELECTED, P(‘E’) =
EFFECTIVE, P(‘E’) =
METHOD, P(‘E’) =
probability that three letters are
the same8
3
9
3
6
1
432
9

48
1

6
1
9
3
8
3

SSEELLEECTCTEEDDEEFFFFEECTIVCTIVEEMMEETHODTHODSELECTEDSELECTED EFFECTIVEEFFECTIVE METHODMETHOD
E
EFFECTIVEEFFECTIVE METHODMETHODMETHODMETHOD

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.
no effect
independent

49. P(A and B) = P(A)  P(B)
where A and B are independent events
and
Condition:
A and B are independent eventsindependent 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
i)P(spaghettP(beef)spaghetti) with P(beef 
6.03.0
18.0
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.
Find the probability that:
(a) I get to work
(b) I do not get to the bus stop in time.
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.
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.

53. Exercise 2 - Solution
up) P(wakeoff) got P(doesn'
up) P(wakeoff) P(go work)P(get to (a)


4
3
)
3
2
1()
6
1
1(
3
2

36
29

4
3
3
1
6
5
3
2

4
1
9
5


54. Exercise 2 - Solution
P(sleep)off) got P(doesn'
P(sleep)off) P(goin time) stop bus get tot P(don' (b)


)
4
3
1()
3
2
1(
6
1
3
2

4
1
3
1
9
1

12
1
9
1

36
7


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
6.05.01.02.03.03.01 
3.002.009.01 
59.0
(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
player) ofP(left )goalkeeper ofP(right -
player) of P(central)goalkeeper of P(central-
player) ofP(right )goalkeeper ofP(left 1



2.05.05.02.03.03.01 
1.01.009.01 
71.0
goal) a hasP(Owen (b)

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:
http://shazam.econ.ubc.ca/flip/index.html
http://www.intergalact.com/threedoor/threedoor.cgi
1. A game flipping a number of coins
2. A game opening one of the three doors