Example: 2 cars, each with a 60% chance of starting. What are the chances that at least one of them starts?
P (A U B) = P(A) + P(B) – P(A Intersection B)
P = .6 + .6 – (.6*.6) = 1.2 – .36 = .84
Mutually Exclusive Events
Mutually exclusive events are things cannot both be true.
Events that are chained together in a row.
Compounded Mutually Exclusive Events
For example, what is the probability of rolling one 6 sided die and getting either a 3 or a 4?
P (A or B) = P(A) + P(B)
P (3 or 4) = P(3) + P(4) = 1/6 + 1/6 = 1/3 = 33%
For example, what is the probability of rolling one 6 sided die twice and getting a 3 on the first roll and a 4 on the second roll?
Since the roll of the second die can be anything – no matter what happens on the first roll – they are considered independent events.
P (A and B) = P(A) * P(B)
P (3 and 4) = P(3) * P(4) = 1/6 * 1/6 = 1/36 = 2.7%