Probability of Atleast One of the Events Occuring

This refers to the addition rule.

The additional rule determines the probability of atleast one of the events occuring.

P (A or B) = P (A) + P (B) - P (A and B)

If A and B are mutually exclusive, then P(A and B) = 0, so the rule can be simplified as follows:

P (A or B) = P (A) + P (B) for mutually exclusive events A and B.

Example

An investor is contemplating buying one of the two stocks A or B. The probability P(A) that an investor will buy stock A is 0.30. The probability P(B) that the investor will buy stock B is 0.50. The probability that he may buy both P(A and B) is 0.10.

The probability that the investor will buy atleast one of the two stocks (A, or B, or both) is calculated as follows:

P(A or B) = 0.30 + 0.50 – 0.10 = 0.70

Suppose P(A) and P(B) are mutually exclusive events, that is, the investor will buy only one of the two stocks, then:

P(A or B) = 0.30 + 0.50 = 0.80