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Determine the
Probability by sample
If S is a sample space and A is an event in the
sample space, then the probability of A happening is:
P(A)=
Range of probability value is: 0 P(A) 1
P(A) = 1 is called a certain event
P(A) = 0 is called an impossible event
)(
)(
Sn
An
Example :
Look at the event of dice throwing.
The outcomes possibility are 1, 2, 3, 4, 5, or 6.
So the sample space is S= {1,2,3,4,5,6}
Suppose the outcomes of even spots dice is
E={2,4,6}.
The number of set E is denoted by n(E),
so n(E)=3
We use the way as follow:
S= {1,2,3,4,5,6} , so n(S) = 6
E= {2,4,6} , so n(E)= 3
P(E)= 2
1
6
3
)(
)(
Sn
En
EXERCISE
there is a dice that will be
tossed. Determine the
probability of appearing:
a. 2
b. Numbers in a dice that
less than 4
c. 7
d. 1, 2, 3, 4, 5, or 6
Expected frequency of an event is a probability
that is done in many times. If A is an event of
an experiment and this experiment is done n
times then the probability of event A in n
experiments is :
Expected frequency
nAPAFh )()(
Example :
1. A coin which consists of the number side and the picture side
tossed 100 times. How many the probability of appearing number
side?
Answer : If the coin is tossed 1 time, the probability of appearing
picture side is 1 / 2. Because the probability of appearing of picture
side for 1 time tossed is 1 / 2, then for tossed 100 times, we will get
:
50100
2
1
)(
)()(
AF
nAPAF
h
h

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Probability Sample Space Events Dice Coin Toss

  • 1. Determine the Probability by sample If S is a sample space and A is an event in the sample space, then the probability of A happening is: P(A)= Range of probability value is: 0 P(A) 1 P(A) = 1 is called a certain event P(A) = 0 is called an impossible event )( )( Sn An
  • 2. Example : Look at the event of dice throwing. The outcomes possibility are 1, 2, 3, 4, 5, or 6. So the sample space is S= {1,2,3,4,5,6} Suppose the outcomes of even spots dice is E={2,4,6}. The number of set E is denoted by n(E), so n(E)=3
  • 3. We use the way as follow: S= {1,2,3,4,5,6} , so n(S) = 6 E= {2,4,6} , so n(E)= 3 P(E)= 2 1 6 3 )( )( Sn En
  • 4. EXERCISE there is a dice that will be tossed. Determine the probability of appearing: a. 2 b. Numbers in a dice that less than 4 c. 7 d. 1, 2, 3, 4, 5, or 6
  • 5. Expected frequency of an event is a probability that is done in many times. If A is an event of an experiment and this experiment is done n times then the probability of event A in n experiments is : Expected frequency nAPAFh )()(
  • 6. Example : 1. A coin which consists of the number side and the picture side tossed 100 times. How many the probability of appearing number side? Answer : If the coin is tossed 1 time, the probability of appearing picture side is 1 / 2. Because the probability of appearing of picture side for 1 time tossed is 1 / 2, then for tossed 100 times, we will get : 50100 2 1 )( )()( AF nAPAF h h