Two events are said to be mutually exclusive (or disjoint events) if they cannot occur at the same time or simultaneously. For two mutually exclusive events there is no elements in common, their intersection is the empty set. Some examples of disjoint events:

• In a deck of 52 cards, drawing a red card and drawing a club are mutually exclusive events because all the clubs are black.
• In a single throw of a dice, either the outcome is an even number or it is an odd number.
• Selecting a number from the set {10, 11, 12, …….., 100}, either the number is a prime number or it is an even number.

If the events \(A\) and \(B\) are mutually exclusive events, then

\(P(A \cap B) = 0\) and \(P(A \cup B) = P(A) + P(B)\)

If \({A_1},\,\,{A_2},\,\,{A_3},\,\,.........,\,{A_n}\) are disjoint events, then

\(P({A_1} \cup {A_2} \cup {A_3} \cup ...... \cup {A_n}) = P({A_1}) + P({A_2}) + ... + P({A_n})\)

In general if the events \(A\) and \(B\) are not mutually exclusive, the probability of getting \(A\) or \(B\), \(P(A \cup B)\)is given by the formula:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)