This document discusses probability and how it is calculated from a sample space. It provides the formula for calculating probability as the number of outcomes in the event divided by the total number of outcomes in the sample space. It gives examples of calculating probability when rolling a die and explains that probabilities range from 0 to 1, with 1 being a certain event and 0 being impossible. It also introduces the concept of expected frequency as the probability of an event occurring over many trials.

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
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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
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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
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)()(
AF
nAPAF
h
h