P(A or B) denotes the probability of occurrence of atleast one of the two events A or B. This probability can be calculated using the well-known addition formula in probability theory.
The addition rule for probability is given as,
Hence, we can calculate the required probability if we know the individual probabilities of occurrence in the above formula.
Example: Suppose a die is thrown. Let A denote the event that we get an even number and let B denote the event that we get a number greater than 2. Calculate the probability that either of the events A or B occur.
Solution: Since the dice has 3 even numbers out of 6 therefore,
P(A) = 3/6 = 1/2
Since the dice has 4 numbers greater than 2 therefore,
P(B) = 4/6 = 2/3
There are exactly two even numbers greater than 2 on the dice therefore,
P(A and B) = 2/6 = 1/3
So P(A or B) = P(A)+P(B)+P(A and B) = 1/2 +2/3 – 1/3 = 5/6
Example: Suppose a card is chosen from a pack of 52 playing cards. Let A denote the event that we get a red card and let B denote the event that we get a king. Calculate the probability that either of the events A or B occur.
Solution: Since the pack of cards has 26 red cards therefore,
P(A) = 26/52 = 1/2
Since the pack has 4 kings therefore,
P(B) = 4/52 = 1/13
There are exactly two red kings therefore,
P(A and B) = 2/52 = 1/26
So P(A or B) = P(A)+P(B)+P(A and B) = 1/2 +1/13 – 1/26 = 0.538
