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Section 7.2
Definition of Probability
m
is the relative frequency of an event E that occurs m times
n
after n repetitions.
Note: The probability of an event is a number that lies between 0 and
1, inclusive.
The ratio
Example 1: A certain town has 5,690 people. A recent survey showed
that 2,308 people wear eyeglasses regularly. What is the probability
that a person chosen at random from this town does not wear
eyeglasses regularly?
If S={s 1 , s 2 ,…, s n } is a finite sample space with n outcomes, then the
events {s 1 }, {s 2 },…, {s n } are called simple events of the experiment.
Example 2: A fair die is cast. List the simple events and the probability
distribution.
Once probabilities are assigned to each of these simple events, we
obtain a probability distribution.
The probabilities, P(s 1 ), P(s 2 ),…, P(s n ) have the following properties:
1. 0 < P(s i ) < 1, i  {1, 2, …, n}
2. P(s 1 ) + P(s 2 ) + … + P(s n ) = 1
3. P(s i  s j ) = P(s i ) + P(s j ), i  j and i, j  {1, 2, …, n}.
Example 3: The accompanying data were obtained from a survey of
500 Americans who were asked: How safe are American-made
consumer products?
Rating
A (Very Safe)
B (Somewhat Safe)
C (Not too Safe)
D (Not Safe at All)
E (Don’t Know)
Number of Respondents
174
199
57
43
27
Section 7.2 – Definition of Probability
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Find the probability distribution associated with this experiment.
A sample space in which the outcomes of an experiment are equally
likely to occur is called a uniform sample space.
Let S={s 1 , s 2 ,…, s n } be a uniform sample space. Then
P(s 1 )  P(s 2 )  ...  P(s n ) 
1
n
Finding the probability of an Event E
1. Determine the sample space S.
2. Assign probabilities to each of the simple events of S.
3. If E={s 1 , s 2 ,…, s k } (k  n), then P(E)  P(s1 )  ...  P(s k ) .
Example 4: A pair of fair dice is cast. What is the probability that
a. The sum of the numbers shown in the uppermost is less
than 3
b. At least one 2 is cast?
Section 7.2 – Definition of Probability
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Example 5: If a marbles is selected at random form an urn containing
six red marble, four blue marbles and seven white marbles. What is the
probability that the marble is red?
Example 6: If one card is drawn from a well-shuffled standard 52-card
deck, what is the probability that the card drawn is
a. a club?
b. a red card?
c. a seven?
d. the ace of spades?
Section 7.2 – Definition of Probability
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