the chinese university of hong kong edd 5161 educational communications and technology group 2...
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THE CHINESE UNIVERSITY OF HONG KONG
EDD 5161
Educational Communications and Technology
Group 2
Instructor: Dr. LEE FONG LOK
ContentsA. Revision
C. Complementary Events
E. Multiplication of Probability
F. Examples
G. Exercises
B. Mutually exclusive events
D. Independent Events
A. Revision
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)=outcomes possible ofnumber Total
event the tofavourable outcomes ofNumber
(1) Definitions
Example 1:
(2) The possible outcomes
An unbiased coin
The total possible outcomes is head (H) or Tail (T)
P(H)=2
1and P(T)=
2
1
An event(E) that is certain to happen, then
P(E) = 1
e.g. A die is thrown
(4) Certain and impossible
P(integers)= 6
6=1
(4) Certain and impossible
An event(E) that is impossible to happen, then
P(E) = 0
e.g. A die is thrown
P(getting a ‘0’) =6
0= 0
P(E) = 0P(E) = 0
0 P(E) 1
certainimpossible
(5) Conclusion
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
0 P(E) 1 0 P(E) 1
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(B) Mutually exclusive eventsTwo 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 B: getting a
Event C: getting a multiple of 3
Which are the mutually exclusive events?
Event A: getting a
Event B: getting a Correct
Answer: A and B
Addition of Probabilities
When two events E and F are mutually exclusive, then
P(E or F) = P(E) + P(F)
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
52
4+
52
4=
2
1
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(C) Complementary EventsGiven an event E, its complementary event E’ is the event that ‘E does not happen’. We have
P(E) + P(E’) = 1
Example:
P(A) + P(B) =1/2 + 1/2 = 1
Event A: getting a head
Event B: getting a Tail
Tossing a coinAre event A and B complementary ?
More example
Eventcomplementary
eventIn a Mathematics Test
Event A: will fail in the test
Event B: will pass in the test
Rolling a die
Event A: getting a ‘6’
Event B: getting an odd number
Drawing a card randomly from a pack of playing cards.
Event A: Getting a red card.
Event B: getting a ‘spade’
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 Maina
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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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Complementary Events
P(E)+P(E’)=1P(E)=1-P(E’)P(E’)=1-P(E)
The probability that John will pass a test is .4
3
The probability that he will not pass the test is .4
1
4
31
F. Example
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.
Example of Complementary Events
AnswerAnswer
(a) P(team A or team B wins) = P(team A wins) + P(team B wins)
(b) P(two teams tie) = 1- P(team A or team B wins) Complementary
Complementary
Events ?Events ?
= 0.25 + 0.3= 0.55
= 1-0.55= 0.45
Multiplication of Probability
P(E and F)=P(E) X P(F)P(E and F)=P(E) X P(F)
For two independentFor two independentevents E and F !events E and F !
Multiplication of Probability
P(E and F)P(E and F)=P(E) X P(F after E has occurred)=P(E) X P(F after E has occurred)
For two dependentFor two dependentevents E and F!events E and F!
Two cards are drawn one after the other at randomTwo cards are drawn one after the other at randomfrom a pack of 52 play cards. The first card drawn from a pack of 52 play cards. The first card drawn is put back into the pack and the pack is shuffledis put back into the pack and the pack is shuffledbefore the second card is drawn. before the second card is drawn. Find the probability thatFind the probability that(a) the first card drawn is a ‘king’ and the second (a) the first card drawn is a ‘king’ and the second card is a ‘club’,card is a ‘club’,(b) both cards drawn are the ‘king’ of clubs.(b) both cards drawn are the ‘king’ of clubs.
Example of Multiplication of Probabilities
(a) P(first king) (a) P(first king)
13
152
4
P(second club)P(second club)
4
152
13
P(first king and second club)P(first king and second club)=P(first king) X P(second club)=P(first king) X P(second club)
52
14
1
13
1
(b)(b) P(first king of clubs)P(first king of clubs)= P(second king of clubs)= P(second king of clubs)
52
1
P(both king of clubs)P(both king of clubs)=P(first king of clubs and second king of clubs )=P(first king of clubs and second king of clubs )=P(first king of clubs) X P(second king of clubs)=P(first king of clubs) X P(second king of clubs)
2704
152
1
52
1
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In a toys factory, two machines X and Y are used toIn a toys factory, two machines X and Y are used toproduce 70% and 30% of a certain model of dollsproduce 70% and 30% of a certain model of dollsrespectively. It is found that 5% of the dolls produced byrespectively. It is found that 5% of the dolls produced byX and 15% of the dolls produced by Y defective. If a dollX and 15% of the dolls produced by Y defective. If a dollis selected at random, find the probability that the selected is selected at random, find the probability that the selected doll isdoll is(a) produced by X and is not defective,(a) produced by X and is not defective,(b) defective. (b) defective.
G. ExerciseG. Exercise
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