Probabilities involving more than one event may be
calculated using the Addition Rule and Multiplication Rule. Those are as
follows:
ADDITION RULE:
If there are several possible events, but only one could occur at any
one time, the probability that one of such events will actually occur at a
given time is the total of the probabilities of each individual event happening
at that time.
If
several events are independent (that is occurrence of any one has no effect on
the probability of the occurrence of the others), the probability that all of
the events will happen is represented by multiplying the probabilities of the
individual events together.
To Illustrate:
Using the following portion of a mortality table, calculate the probability
that a person age 40 will die either at age 60 or at age 61.
Age (x)

l_{x}

d_{x}

40

97353

198

41

97155

216

.
.
.

.
.
.

.
.
.

60

84650

1325

61

83325

1406

62

81919

1491

Solution:
Since only one of the events can occur, the Addition Rule
that two individual probabilities are added is applicable. The probability that
a person age 40 will die during the year he or she is age 60 is equal to the
number of people dying at age 60 divided by the number living at age 40:
Basic equation:
Substitute the values from the given
table:
(Probability
of Dying at Age 60) =
1325/97353
(Probability of Dying at Age 60) = 0.0136
Similarly, the probability that a person age 40 will die
during the year he or she is age 61 is
Basic equation:
Substitute the values from the table
(Probability of Dying at age 61) = 1406/97353
(Probability of Dying at age 61) = 0.0144
The desired probability equals the total of the two
individual probabilities:
The equation is:
Hence, 0.0280 is the probability that a
person age 40 will die either at age 60 or 61.
To Illustrate:
Using the following portions of a mortality table, calculate the probability
that a mother age 55, and her daughter, age 25 will both live at least 15 more
years.
Age (x)

l_{x}

24

9953

25

9947

26

9940

.
.

.
.
.

39

9827

40

9814

41

9801

.
.
.

.
.
.

54

9444

55

9388

56

9327

.
.
.

.
.
.

69

7885

70

7717

71

7539

Solution:
Assuming that one event has no effect on
the other, the Multiplication Rule, that two individual probabilities are
multiplied is applicable. For mother;
Basic
equation:
For
Daughter:
The desired probability that both will
live at least 15 years equal the two individual probabilities multiplied
together:
The equation is:
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