COMPREHENDING PROBABILITY

In working around comprehending probability, I realized that before navigating through the numbers which sometimes can be ambiguous and overwhelming, it would be helpful to understand the terms involved. These are some of the few that are a must know in probability.

Union of events

Simply put, this is the chance of any (one or more) of two or more events occurring is called the union of the events.

To get the probability of the union of two events, we use the addition law which is the sum of the individual probability minus the sum of their intersection.

So, the way I devised to make these terms clearer is that union is “either-or” while the intersection is “and”.

Conditional probability

This is defined as the possibility of an event or outcome occurring based on the occurrence of a previous event or outcome.

In understanding conditional probability, the figure that is given is referred to as prior.

It makes a lot of assumptions

First thing is to find conditional probability.

Example P(A/B) = P(AnB)/P(B). Given that B has happened, therefore B is prior.

The rule in solving conditional probability is: You do joint/prior.

The opposite of conditional probability is unconditional probability. In unconditional probability it refers to the possibility that an event will take place whether or not any other events have taken place or any other conditions are given.

Contingency table

A contingency table is used to classify outcomes and calculate different types of probabilities. They are made up of rows and columns and can also be called crosstabulation or frequency tables.

The numbers at the margins is called marginal probability. The ones inside the table is called joint probability. Thus in comprehending probability and how contingency table works:

First thing to do when given a probability problem in its raw values is to convert it to a probability table, it is called a contingency table. Before it is converted, it is in the raw value. The method of converting it is by dividing all the numbers by the total value.

Joint probability is where two events are mutually exclusive. They do not have an intersection therefore addition law would just be adding the two events.

Independent Events: if the probability of event A is not changed by the existence of event B, we would say that events A and B are independent.

For example, in flipping a coin, you either get a head or a tail, both events are independent of each other. In independent events, the event is unaffected by the occurrence of the other. The probability of an event given the prior is the same thing as the probability of the event. It means that the prior has no influence on it and therefore they are independent events.

Mutually exclusive events

This means that the two events do not come or occur together. If A happens, B will not happen at the same time. The probability of both occurring at the same time is equals to zero.

For example, something cannot be hot and cold at the same time, when you toss a coin, it cannot show you heads and tail at the same time.

These are some of the major probability terms and understanding them has aided me in getting into the equations that are attached to them and thus comprehending probability as a whole