Probability

Probability is that branch of mathematics that determines the chance of something happening when other possibilities are included. Probability starts with some basic axioms:

1. 0 ≤ P(x)

The probability is represented by the P. The x represents the event. The probability is always 0 or positive. There cannot be a negative probability. At least not yet.

2. P(x) ≤ 1

The probability cannot be greater than 1. If the probability is one, the event in question will happen no matter what. If the probability was .5, then the chances of the event happening would be 50-50 or 50 percent.

3. P(x^c) = 1 - P(x)

The ^c represents the complement of x or not x. In other words, it is the probability of x not happening and is the probability left over when the probability of x is taken away.

When two events are taken into consideration, their probabilities can combine in different ways. For example, the chances of two events both happening can be said to be an intersection of those events. The symbol for an intersection is .

The chances of one event happening or the other is the union of the two events. If A or B can happen, then their probabilities are added.

Mutual Exclusion

If two events are mutually exclusive, then they do not overlap. Usually, only one event or the other can happen at one time. An example of this would be the side that shows up after rolling dice. For finding the probability of one event happening or the others when all events are mutually exclusive, just add the probability of each event.

P( A ∪ B ∪ C ) = P(A) + P(B) + P(C)

Independence

Two or more events are independent if the chances of one event happening does not affect the chances of the other events happening. For example, rolling dice a second time is not affected by the first roll. The chances of getting a 6 the second time is the same as the first.

The probability of getting different events to different times when they are independent is calculated as follows:

P( A ∩ B ) = P(A) × P(B)

Conditional probability might have to be used when the occurrence of the next event depends upon the event that has just occurred.