THE CHINESE UNIVERSITY OF HONG KONG

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THE CHINESE UNIVERSITY OF HONG KONG EDD 5161
Educational Communications and Technology Group 2
Instructor Dr. LEE FONG LOK
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Group Members
NG TAT YEUNG (S98036770) POON KIN MAN
(S98115970)
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Mathematics Probabilities
Target audience F5 student
Type of software Lecturing
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PROBABILITIES
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Contents
A. Revision
B. Mutually exclusive events
C. Complementary Events
D. Independent Events
E. Multiplication of Probability
F. Examples
G. Exercises
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A. Revision
(1) Definitions
When all possible outcomes under consideration
are equally likely to happen, then the
probability of the happening of an event E, P(E)
is given by
P(E)
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(2) The possible outcomes
Example 1
An unbiased coin
The total possible outcomes is head (H) or Tail
(T)
P(H)
and
P(T)
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Example 2 A Fair die
Total possible outcomes is 6
P( )
Odd numbers
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(3) Special Dice
What is the possible outcome of the above case?
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Example 3
There are 5 red marbles, 3 green marble and 2
black marbles
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P( )
red marbles
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(4) Certain and impossible
An event(E) that is certain to happen, then
P(E) 1
e.g. A die is thrown
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P(integers)
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(4) Certain and impossible
An event(E) that is impossible to happen, then
P(E) 0
P(E) 0
P(E) 0
e.g. A die is thrown
P(getting a 0)
0
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(5) Conclusion
0 ? P(E) ? 1
0 ? P(E) ? 1
0 ? P(E) ? 1
certain
impossible
When the probability is greater than 0.5, implies
the event is likely to happen
When the probability is smaller than 0.5, implies
the event is unlikely to happen
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(B) Mutually exclusive events
Two events are said to be mutually exclusive
events if both events cannot happen at the same
time.
Example
A die is rolled
Event A getting a
Event A getting a
Answer A and B
Event B getting a
Event B getting a
Correct
Event C getting a multiple of 3
Which are the mutually exclusive events?
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Addition of Probabilities
When two events E and F are mutually exclusive,
then
P(E or F) P(E) P(F)
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Example
If a card is drawn at random from a pack of 52
playing cards, find the probability that
Either a king or a queen is drawn
P(king or queen)
P(king) P(queen)
king
queen


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(C) Complementary Events
Given an event E, its complementary event E is
the event that E does not happen. We have
P(E) P(E) 1
Example
Tossing a coin
Are event A and B complementary ?
Event A getting a head Event B getting a Tail
P(A) P(B) 1/2 1/2 1
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More example
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D. Independent Event
The occurrence of one event does not affect the
probability of the occurrence of the other are
simply called independent events.
Event A Getting a head of a coin
Event B Getting a 1 of a die
A and B are independent events
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E. Multiplication of Probability
For two independent events E and F,
P(E and F) P(E) ? P(F)
P(E and F) P(E) ? P(F)
P(E and F) P(E) ? P(F)
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F. Example
Complementary Events
P(E)1-P(E) P(E)1-P(E)
P(E)P(E)1
The probability that John will pass a test is
The probability that he will not pass the test is
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Example of Complementary Events
In a soccer match between two teams A and B, the
probability that team A will win is 0.25 and
probability that team B will win is 0.3. Find
the probability that (a) team A or team B will
win the match, (b) the two teams tie.
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Answer
(a) P(team A or team B wins) P(team A
wins) P(team B wins)
0.25 0.3 0.55
(b) P(two teams tie) 1- P(team A or team B
wins)
Complementary Events ?
1-0.55 0.45
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Multiplication of Probability
For two independent events E and F !
P(E and F)P(E) X P(F)
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Multiplication of Probability
For two dependent events E and F!
P(E and F) P(E) X P(F after E has occurred)
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Example of Multiplication of Probabilities
Two cards are drawn one after the other at
random from a pack of 52 play cards. The first
card drawn is put back into the pack and the
pack is shuffled before the second card is drawn.
Find the probability that (a) the first card
drawn is a king and the second card is a
club, (b) both cards drawn are the king of
clubs.
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(a) P(first king)
P(second club)
P(first king and second club) P(first king) X
P(second club)
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(b) P(first king of clubs) P(second king of
clubs)
P(both king of clubs) P(first king of clubs
and second king of clubs ) P(first king of
clubs) X P(second king of clubs)
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G. Exercise
In a toys factory, two machines X and Y are used
to produce 70 and 30 of a certain model of
dolls respectively. It is found that 5 of the
dolls produced by X and 15 of the dolls produced
by Y defective. If a doll is selected at random,
find the probability that the selected doll
is (a) produced by X and is not defective, (b)
defective.
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