Addition law probability
May 31, 2022, 16:45 IST
Addition law probability
Definition :-The addition law of probability (sometimes referred to as the addition rule or sum rule), states that the probability that a or b will occur is the sum of the probabilities that a will happen and that b will happen, minus the probability that both a and b will happen. The addition rule is summarized by the formula:
P(A∪B) = P(A)+P(B)−P(A∩B)
Addition Rule for Disjoint Events
Suppose A and B are disjoint, their intersection is empty. Then the probability of their intersection is zero. In symbols:
The addition law then simplifies to:
The symbol
represents the empty set, which indicates that in this A and B do not have any elements in common (they do not overlap).
Example 1 :-Suppose a card is drawn from a deck of 52 playing cards: what is the probability of getting a king or a queen?
Solution :-Let A represent the event that a king is drawn and B represent the event that a queen is drawn. These two events are disjoint, since there are no kings that are also queens. Thus:
Example 2 :-If you take out a single card from a regular pack of cards, what is probability that the card is either an ace or spade?
Solution :-
Let X be the event of picking an ace and Y be the event of picking a spade.
The two events are not mutually exclusive, as there is one favorable outcome in which the card can be both an ace and spade.
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