CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 3. An Introduction to Probability

This figure shows that the eventsAandBhave no simple events in common, that is, eventsAandBcan not occur
simultaneously, and therefore,P(A∩B) = 0.

If the eventsAandBaremutually exclusive,then the probability of the union ofAandBis the sum of the
probabilities ofAandB, that is

P(A∪B) =P(A)+P(B)

Notice that since the two events are mutually exclusive, there is no over-counting.

Example:

If two coins are tossed, what is the probability of observing at least one head?

Solution:

Let

A:{observe only one head}

B:{observe two heads}

P(A∪B) =P(A)+P(B) = 0. 5 + 0. 25 = 0. 75 =75%

Recall from previous section that the conditional probability rule is used to compute the probability of an event,
given that another event had already occurred. The formula is

P(A|B) =

P(A∩B)

P(B)

Solving forP(A∩B), we get

P(A∩B) =P(A)P(A|B)

This result is theMultiplicative Rule of Probability.