The increasing level of uncertainty prevalent in our today’s world has brought us to that point where the use of probability will be our daily companion and this is so because of the need for proper planning in business and life generally. Planning and projecting for the future is characterized by uncertainties but that does not suggest that we abandon the planning rather with experience and learning future occurrences can be determined with high probable prediction, hence the concepts of probability.
Probability is the state or quality of being probable, it is the extent of likelihood to which an event will occur or otherwise. Probability is subject to changes and expectations. It is a study or branch of Mathematics that studies the chances that a given possible outcome will occur and it is calculated as the ratio of the number of outcomes that produces a given event to the total number of possible outcomes. The lower the probability calculated, the less likely the event to occur and the higher the probability, the higher the likelihood of occurrence of the event.
Applying the concepts of probability will require adherence to its established rules and which include:
Rule 1: The Probability for any given event A is 0 ≤ P(A) ≤ 1: The probability of an impossible event is zero; the probability of a certain event is one. Therefore, for any event A, the range of possible probabilities is: 0 ≤ P(A) ≤ 1.
Rule 2: The sum of the probability of all possible outcomes is equal to 1: For S, the sample space of all possibilities, P(S) = 1. That is the sum of all the probabilities for all possible events is equal to one. Recall the party affiliation above: if you have to belong to one of the three groups (A, B, or C), then the sum of P(A), P(B), and P(C) is equal to one.
Rule 3: The compliment Rule: For any event A, P(Ac) = 1 – P(A). It follows then that P(A) = 1 – P(Ac).
Rule 4: The Addition Rule: This is the probability that either one or both events occur:
a. If two events, say A and B, are mutually exclusive – that is A and B have no outcomes in common – then P(A or B) = P(A) + P(B).
b. If two events are NOT mutually exclusive, then P(A or B) = P(A) + P(B) – P(A and B).
Rule 5: Multiplication Rule: This is the probability that both events occur.
a. P (A and B) = P(A) • P(B|A) or P(B)*P(A|B). Note: this straight line symbol, |, does not mean divide! This symbol means “conditional” or “given”. For instance, P(A|B) means the probability that event A occurs given event B has occurred.
b. If A and B are independent – neither event influences or affects the probability that the other event occurs – then P(A and B) = P(A)*P(B). This particular rule extends to more than two independent events. For example, P(A and B and C) = P(A)*P(B)*P(C).
Rule 6: Conditional Probability: This is expressed as P(A|B) =P(A – B)/P(B) OR
P(B|A) = P(A –B)/P(A).