Multiplication

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 teachers
instructions.
Its 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
5 Summary
6 Exercises
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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
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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
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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
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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
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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
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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
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Contents
1 Revision
Some word to say
3 Multiplication of Probability
2 Independent Events
4 Examples
5 Summary
6 Exercises
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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
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1. Revision
I) Definition of Probability
Example The possible outcomes
?

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

2
3
1
4
9
9
5
7
6
8
15
1. Revision
I) Definition of Probability
Example The possible outcomes
1
3
3
1
2
?

3
9
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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
Example A coin is tossed.
P(head or tail)
1
Since the possible outcomes are
5
and
and they are also favourable outcomes.
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1. Revision
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
Example A die is thrown.
P(getting a 7)
0
Since the possible outcomes are
,
,
,
,
and
impossible
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1. Revision
IV) 0 P(E) 1
0 1/2 1
evenly likely
certain
impossible
unlikely
likely
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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.
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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.
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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.
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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.
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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?
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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.
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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.
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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?
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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.
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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.
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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?
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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.
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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.
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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)
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3. Multiplication of Probability
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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 ?
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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
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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
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3. Multiplication of Probability
What is the probability of getting a head and an
odd number?
P(H and Odd)
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3. Multiplication of Probability
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3. Multiplication of Probability
Find the probability that one die shows an Odd
number and the other die shows a number
divisible by 3.
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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)
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3. Multiplication of Probability
Condition!?
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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?
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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

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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?
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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?
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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.
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Which letter should be choose
SELECTED
EFFECTIVE
METHOD
EFFECTIVE
METHOD
METHOD
SELECTED
EFFECTIVE
METHOD
E
probability that three letters are the same
SELECTED, P(E)
EFFECTIVE, P(E)
METHOD, P(E)
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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
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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
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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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Exercise 1- Solution
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Exercise 2
My old alarm clock has a probability of 2/3 that
it will go off.
If it doesnt, there is still a probability of
3/4 that Ill wake up anyway in time to catch
the 8 oclock bus.
Even if it does go off, there is a probability of
1/6 that Ill 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.
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Exercise 2 - Solution
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Exercise 2 - Solution
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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.
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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)
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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.
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Exercise 3 - Solution
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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.
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Exercise 3
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Some interest web page related to probability
1. A game flipping a number of coins
http//shazam.econ.ubc.ca/flip/index.html
2. A game opening one of the three doors
http//www.intergalact.com/threedoor/threedoor.cgi
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Thank you and Good bye