# Probability Equations

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Probability is defined as the chances for an event to occur. For a given situation or conditions there is always a chances for an event to likely or unlikely occur. The probability of an event is mostly in-between 0 to 1. The chances or probability for all the possible events to occur for a given condition add up to a 1. Therefore probability of an event is calculated by the following formulas:
P (E) = Number of outcomes favorable for the event/Total number of outcomes.
P (not E) = 1 – P (E). Therefore P (E) + P (not E) = 1.

Example 1: A dice is thrown what is the probability of getting the number 7?

Solution: On throwing a dice the total number of possibilities are 6 either of the following numbers may show up i.e. {1, 2, 3, 4, 5, and 6}.

Therefore total number of possible outcomes on throwing a dice = 6.

The number of outcomes favorable of getting the number 7 = 0.

P (7) = Number of outcomes favorable for number 7/Total number of outcomes. = 0/6.

Therefore probability of getting number 7 is P (7) = 0.

Example 2: A dice is thrown what is the probability of not getting the number 5?

Solution: Total number of possible outcomes on throwing a dice = 6.

The probability of getting number 5 is P (5) = 1/6.

Using the formula P (not E) = 1 – P (E). P (not 5) = 1 – 1/6 = 5/6.

Therefore probability of not getting number 5 is 5/6.