# Multiple Event Probability Tutorial

## Multiple Event Probability

##### Probability Definition:

Probability is used to find the number of occurrence of an event out of possible outcomes. Probability should always lies between 0 and 1.

##### Multiple-event probability definition:

Multiple Event probability is used to find the probability for multiple events that occurs for an experiment. For example, consider tossing a coin twice, we may get head at first time and tail at second time. Here two events are not occurring together and this type of events occurring is said to be mutually exclusive events.

#### Formula:

Probability that event A occurs P(A) = n(A) / n(S). Probability that event B occurs P(B) = n(B) / n(S).
###### where,

n(A) - number of event occurs in A n(S) - number of possible outcomes n(B) - number of event occurs in B Probability that event A does not occur P(A') = 1 - P(A). Probability that event B does not occur P(B') = 1 - P(B). Probability that both the events occur P(A ∩ B) = P(A) x P(B). Probability that either of event occurs P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Conditional Probability P(A | B) = P(A ∩ B) / P(B).

##### Example:

Consider, a die is thrown twice. Calculate the probability of getting odd numbers and even numbers from the events?

###### where,

n(A) = occurrence of odd numbers = 3 , n(B) = occurrence of even numbers = 3, n(S) = total number of sample space = 6. P(A) = n(A) / n(S) = 3 / 6 = 0.5. Probability that event A occurs = 0.5. P(B) = n(B) / n(S) = 3 / 6 = 0.5. Probability that event B occurs = 0.5. P(A') = 1 - P(A) = 1 - 0.5 = 0.5. Probability that event A does not occur = 0.5. P(B') = 1 - P(B) = 1 - 0.5 = 0.5. Probability that event B does not occur = 0.5. P(A ∩ B) = P(A) x P(B) = 0.5 x 0.5 = 0.25. Probability that both the events occurs = 0.25. P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.5 + 0.5 - 0.25 = 0.75. Probability that either of event occurs = 0.75. P(A | B) = P(A ∩ B) / P(B) = 0.25 / 0.5 = 0.5. Conditional probability of A given B = 0.5.

This tutorial will guide you to calculate basic probability distribution for multiple events.