Probability

Probability is a numerical statement about the likelihood that an event will occur. It is generally used to describe how the mind’s approach regarding some proposition of whose truth is not definite.  We ask ourselves if a specific event will occur, how confident are we that this will occur? The certainty we implement can be portrayed through numerical measure, wherein probability can be called as the number, between 0 and 1. Mutually exclusive and collectively exhaustive are very important aspect of probability theory. Events can be considered as mutually exclusive if two events have no common outcome. It is impossible for two or more events to happen at the same time. The probability of the first or the second event occurring alone can be determined by getting the sum of their probabilities. Two statements are contradictories when they cannot both be true, and cannot both be false. Also, It is called mutually exclusive if the two event's probabilities happening at the same time is zero. For example, if you roll a six-sided die once, the result would either be rolling an odd or even number. Notice that these events cannot occur at the same time. Another example is when tossing a fair coin, the result of getting a head and getting a tail are mutually exclusive because they cannot occur at the same time (Render, Stair, & Hanna, 2011).

On the other hand, events are considered collectively exhaustive if everything is comprised in at least one event. It only means that the list of items covered thoroughly addresses the problem and that one of them must occur, which totals the probability to 1. An example to this is when you roll a six-sided die; you will get 1, 2, 3, 4, 5, or 6 as a result. Another is when tossing a coin; you will get either a head or tail (Rasiel, 1999).

In the business world, usually when predictions failed, we would ask ourselves what caused the circumstance to have unexpected outcome and why it happened? In order to analyze this...