Download 12.4 Probability of Compound Events

12.4 Probability of Compound
Events
Algebra 2
Probabilities of Unions and
Intersections
Union of A and B: all the outcome of two
events A and B
 Intersection of A and B: Only the
outcomes shared by both A and B
 Compound Events: The union or
intersection of two events
 Mutually exclusive events: When no
outcomes are shared by A and B.

Probability of Compound Events

If A and B are two events, then the
probability of A or B is:
P(A or B) = P(A) + P(B) – P(A and B)

If A and B are mutually exclusive, then the
probability of A or B is:
P(A or B) = P(A) + P(B)
Examples:

One six-sided die is rolled. What is the
probability of rolling a multiple of 3 or 5

One six-sided die is rolled. What is the
probability of rolling a multiple of 3 or a
multiple of 2?
Example:

In a poll of high school juniors, 6 out of 15
took a French class and 11 out of 15 took
a math class. Fourteen out of 15 students
took French or math. What is the
probability that a student took both
French and math?
Examples:

In a survey of 200 pet owners, 103 owned
dogs, 88 owned cats, 25 owned birds, and
18 owned reptiles.
◦ None of the respondents owned both a cat
and a bird. What is the probability that they
owned a cat or a bird?
◦ Of the respondents, 52 owned both a cat and
a dog. What is the probability that a
respondent owned a cat or a dog?
Example continue:

In a survey of 200 pet owners, 103 owned
dogs, 88 owned cats, 25 owned birds, and
18 owned reptiles.
◦ Of the respondents, 119 owned a dog or a
reptile. What is the probability that they
owned a dog and a reptile?
Using Complements
Complement: consists of all outcomes
that are not in event A (called A’)
 Probability Of The Complement Of An
Event

◦ The probability of the complement of A is
P(A’) = 1 – P(A)
Example:

A card is randomly selected from a
standard deck of 52 cards. Find the
probability of the given event.
◦ The card is not a king.
◦ The card is not an ace or a jack.
Example:

One high school requires students to
complete 30 hours of community service
to graduate. There are 156 different
community service options to choose
from. What is the probability that in a
group of 5 students, at least 2 of them will
be doing the same service.
Example:

Seven prizes are being given in a raffle
contest. 157 tickets are sold. After each
prize is called, the winning ticket is
returned to the drawing box and is
eligible to be picked for anther prize.
What is the probability that at least one
of the tickets is drawn twice?