Section 7.2
Definition of Probability
The ratio
n
m
is the
relative frequency
of an event E that occurs m times after n
repetitions.
Note:
The probability of an event is a number that lies between 0 and 1, inclusive.
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 , s ,…, s
} is a finite sample space with n outcomes, then the events {s
},
{s },…, {s
} are called
simple events
of the experiment.
1
2
n
1
2
n
Example 2:
A fair die is cast.
List the simple events.
Once probabilities are assigned to each of these simple events, we obtain a probability
distribution.
The probabilities, P(s
1
), P(s
),…, P(s
) have the following properties:
2
n
1.
0 <
P(s
i
) <
1,
i
∈
{1, 2, …,
n
}
2.
P(s
1
) + P(s
) + … + P(s
) = 1
2
n
3.
P(s
s
) = P(s
i
) + P(s
),
i
U
i
j
j
≠
j
and
i, j
∈
{1, 2, …,
n
}.
Example 3: