Example #1d: Two Events: Addition (‘Or’) Law

Part d) demonstrates how to calculate the probability of the union of two events. If A is an event and B is another event, then P(A or B) is the probability of either A occurring, orB occurring, or both occurring. ‘Or’ is commutative in the sense that P(A or B) = P(B or A).

The following formula is used to find P(A or B):

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

This is the general case of the Addition Law.

For example, if the event is selecting a Red or an Odd marble, then:

P(Red or Odd) =P(Red) + P(Odd) - P(Red and Odd)
= 4/20 + 10/20 - 4/20
=10/20

The Addition Law simplifies if A and B are mutually exclusive. In this case:

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

since P(A and B) = 0.

Use the applet to compute the probabilities of the union of other events and observe which marbles are in the union. What happens if you select Red or Even? Compare this latter event with Blue or Even.

Part a): Basic Probability

Part b): Conditioning

Part c): And Law

Example #1