Page 32 - Insurance Times April 2023

Classical probability: Compound Probability:
It is the statistical concept that measures the likelihood It refers to a mathematical calculation that determines
(probability) of something happening. In a classic sense, the possibility of two separate events happening at the
it means that every statistical experiment will contain same time. To calculate compound probability, multiply
elements that are equally likely to happen (equal chances the possibility of the first event occurring with the
of occurrence of something) probability of the second event occurring.
Objective Probability: The insurance industry uses compound probability to
analyses risks and determine premiums.
It refers to the chances or the odds that an event will
occur based on the analysis of concrete measures rather To use a simple example, suppose we knew someone
than hunches or guesswork. Each measure is a recorded who went for a morning jog 50% of the time and who
observation, a hard fact, or part of a long history of also drove their car on average every other day. If we
collected data. wanted to calculate the compound probability of them
doing both activities on the same day, we would multiply
It refers to long-run relative frequency of an event based
both percentages, as follows:
on the assumptions of an infinite number of observations
and of no change in underlying conditions. It also 0.5 x 0.5 = 0.25 This means there is a 25% chance that
ascertains that the occurrence of an event on the basis this person would both go for a jog and drive their car on
a given day.
of already present information or observation or large
portion of accumulated data. Marginal probability:

Subjective probability: (personal probability) It is the probability of an event irrespective of the
outcome of another variable. It is the probability of
It is the individual's personal estimate of the chance of
occurrence of a single event. In calculating marginal
loss and is based on your beliefs. The probability of an
probabilities, we disregard any secondary variable
event is a "best guess" by a person making the statement
calculation. In our hypothetical example, we can
of the chances that the event will happen. (e.g. 30%
calculate two marginal probabilities, we can look at
chance of rain)
specific eating habits or we can look at commute times.
It permits the analyst to calculate the probability of an
In essence, we are calculating the probability of one
outcome based on experience and their own judgement.
independent variable. It is not conditioned on another
This type of probability is the perceived chance of a event.
certain outcome happening. It is not an actual
Joint probability:
mathematical calculation of the odds, but rather a
It is the joint probability which is the probability of two
measure based on personal opinion, beliefs, prejudices,
different events occurring at the same time or
and emotions.
simultaneously .
For example, a fan of the favourite game say their team
It is the probability of the intersection of two or more
has a 50% chance of winning the World Series, despite
events. The probability of the intersection of A and B
not having any statistical evidence. It is not based on the
may be written p (A ? B). Example: the probability that a
team's record, but on the fan's personal beliefs and
card is a four and red =p (four and red) = 2/52=1/26.
confidence. (There are two red fours in a deck of 52, the 4 of hearts
and the 4 of diamonds).
Experimental or empirical probability:
It is expressed as a ratio of the number of times an event Conditional probability:
as occurred and the number of experiments performed. It is the probability that an event will occur given that
The method becomes increasingly accurate the more another specific event has already occurred. For
experiments are conducted, which translates into bigger example, we would calculate the probability for some
and more revealing data. It is also based upon eating behaviour given that we know the commute times
experiments. of the population. We say that we are placing a condition
on the larger distribution of data, or that the calculation
This method helps insurers predict the likelihood of claims
for one variable is dependent on another variable. It is
being filed so they can make informed decisions about
the probability of one event occurring in the presence of
premium rates. It is a statistical method for determining
a second event.
the frequency of an event by using actual data from
experiments. Conditional probability is the probability of one event
28 April 2023 The Insurance Times