Page 11 - Life Insurance Today March 2016

In studying death rate of human life, we have to fall back
on the statistical definition only. Considering a group of
10,000 lives aged 35 years, observed for one year. If 13
die before expiry of one year, the death rate at age 35 is
13/10000 = 0.0013.
When the number of lives observed is increased,it may
tend to a certain value say .00124. Then this value is taken
as probability of dying within one year at age 35. It is
denoted by Q35 and is known as the mortality rate at age
35. Thus, Q35 = .00124. So for calculation of net premiums
in life policies, we need to depend on the probability and
mortality tables to assurance values.
The life insurers while fixing the premium rates or
assessing the liabilities under the Life Insurance contracts
has to make certain assumptions regarding interest rates,
mortality rates and expenses which will be experienced in
the years to come. It is important to have a correct
estimate of these factors as otherwise the results deduced
from the assumptions made may not be reasonably close
to the actual experience of the insurers.
E. Properties of probability applicable in
life insurance:
(1) Probability of happening of an event is a fraction lying
between 0 and 1, as in relative frequency 'N/M'; 'N'
cannot exceed 'M'. If the probability is '0' it means that
the event cannot happen, whilst if it is 1, it means that
the event is certain to happen.
(2) If the probability that event 'E' happens is 'P', the
probability that the event does not happen is (1-P).
In other way, (1-P) is exactly the probability of the
event "non-E" happening. Thus, if in case of throwing
a dice the probability that the number 1 turns up is
1/6, the probability that the number is not turning up
is (1- 1/6) or 5/6. Again if the probability that a person
aged 30 dies within a year is 0.001; the probability
that a person aged 30 does not die within a year (i.e.
survives for one year) is 0.999. Two such events are
called "Complementary events". If the probability of
an event is known the probability of the
complementary event is obtained by subtracting this
probability from unity (i.e. 1).
"Darkness cannot drive out darkness: only light can do that. Hate cannot drive out hate: only love can do that."
Life Insurance Today March 2016
(3) If 'P' is the probability of an event to occur, (1-P) is
complementary probability that the event will not
occur and is denoted as 'Q'. In other words P + Q = 1,
i.e. the sum of Probabilities of two complementary
events is unity (i.e. 1).
(4) It follows the Addition Theorem of Probability- It can
be explained by the following example:
Example: A bag contains 8 balls, viz, 1 black, 3 red and
4 yellow balls. What is the probability for an event E
that a ball drawn is either black or red?
a. Probability (P) = No. of favourable ways / Total no.
of mutually exclusive & exhaustive events.
b. The number of favourable ways is 4 because there
are 1 black and 3 red balls and any one of them
when drawn will be considered as favourable for
happening of the given event. Also total number
of equally likely exclusive and exhaustive ways in
which balls can be drawn is 8 as there are only 8
balls are in the bag. Therefore, P = 4/8 = ½
c. If we define event E1 as that of drawing a black
ball and E2 as that of drawing a red ball and if the
corresponding probabilities of happening these
events when a ball is drawn are denoted by P1
and P2 respectively then events E1 and E2, are
mutually exclusive because both of them cannot
occur simultaneously. Also P1 i.e. probability that
a ball drawn is black = 1/8 and P2 i.e. probability
that the ball drawn is red = 3/8. We observe that
P1+ P2 = 1/8 + 3/8 = 4/8 = ½ = P.
d. When two events E1 and E2 are mutually exclusive
and if P1 is the probability for occurrence of event
E1 and P2 is the probability for occurrence of event
E2 then the probability that either event E1 or
event E2 will occur is given by P1+P2. This is known
as Addition Theorem of Probability.
e. The Addition Theorem can be extended to more
than 2 events. Thus if the probabilities of mutual
events E1, E2, E3 to occur be P1, P2, P3
respectively then probability that either E1 or E2
or E3 happens is given by P1+P2+P3.
f. It may also be noted that the result does not hold
good if the events are not mutually exclusive. For
example let us consider a case of throwing a dice.
Let event E1 be defined to occur when it turns up
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