36 2. FUNDAMENTAL RELIABILITY MATHEMATICS
Solution:
Let A represent the event of the sum of the showing number equal to 5, that is, A D
f
5
g
. is
event A contains four possible sample points:
.
1 C 4
/
;
.
2 C 3
/
;
.
3 C 2
/
, and
.
4 C 1
/
. e prob-
ability of P
.
f
5
g
/
will be:
P
.
f
5
g
/
D
4
36
:
en, the probability of the sum of the showing numbers not equal to 5 is
P
A
D 1 P
.
A
/
D 1
4
36
D
8
9
:
2.5.5 PROBABILITY OF STATISTICALLY INDEPENDENT EVENTS
Statistically independent events: If the occurrence of the event E
1
in no way affects the prob-
ability of occurrence of the event E
2
, the events E
1
and E
2
are statistically independent events.
An example of two statistically independent events are rolling dice and tossing a coin.
When two events E
1
and E
2
are statistically independent, the intersection of events E
1
and E
2
just means that both occur. e probability of the intersection of two statistically inde-
pendent event E
1
and E
2
will be equal to the multiplication of probabilities of each event, that
is,
P
.
E
1
E
2
/
D P
.
E
1
/
P
.
E
2
/
: (2.20)
Example 2.16
ere is a total of seven balls in a box including three red balls and four green balls. Randomly
pick one ball from the box, record the color, and put it back. Calculate the probability of the red
ball in the first picking and the blue ball in the second picking.
Solution:
Let event E
1
to represent the red ball in the first picking and event E
2
the blue ball in the second
picking.
e probability of the event E
1
, that is, red ball in first picking will be:
P
.
E
1
/
D
3
7
:
e probability of the event E
2
, that is, blue ball in second picking will be:
P
.
E
2
/
D
4
7
:
In this problem, the ball will be put back into the box. erefore, these two events E
1
and E
2
are statistically independent. So, according to Equation (2.20), the probability of the red ball in
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