April 14, 2016
April 14, 2016
(13.6) Probabilities of Mutually Exclusive Events
Objective: To determine the probabilities of mutually exclusive events and nonmutually exclusive events.
To determine the probabilities of complements.
Why: The study of probabilities can lead to understanding concepts in graph
theory.
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
Mutually Exclusive Events:
events that can NOT happen at the same time
(they have no outcomes in common)
Ex.1 Determine whether the events are Mutually Exclusive.
At a HS, any grade 9-12 can run for Student Council President.
a. a junior winning the election or a senior winning the election.
b. a sophomore winning the election or a female winning the election.
c. drawing an ace or a club from a standard deck of cards.
d. selecting a number at random from the integers 1-100 and getting a number
divisible by 5 or a number divisible by 10.
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
Probability of Mutually Exclusive Events:
Ex.2
a. A die is rolled, what is the probability of getting a 3 or a 4?
b. Tim reaches into a can that contains 30 quarters, 25 dimes, 40 nickels, and
15 pennies. What is the probability that the first coin he picks is a quarter or
a penny?
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
Question:
To determine the probabilities of complements.
A die is rolled. What is the probability of getting a number greater than 2 or
an even number?
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
Probability of Events that are NOT Mutually Exclusive:
A
B
(A and B)
P(A or B) = P(A) + P(B) - P(A and B)
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
What is the probability that Namiko will select a portrait or an oil painting?
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
What is the probability of drawing a king or a diamond from a standard deck
of 52 cards?
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
The complement of an event A:
consists of all the outcomes in the sample space that are not included as
outcomes of event A.
Ex. If a die is rolled, what is:
a. P(4)
b. P(not 4)
Probability of the Complement of an Event:
P(not A) =
1 - P(A)
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
Mike bought 15 chances to pick one red marble from a container to win a gift
certificate to the bookstore. If there is a total of 200 marbles in the
container, what is the probability that Mike will not win the gift certificate?
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
April 14, 2016
Obj: To determine the probabilities of mutually exclusive events and
non-mutually exclusive events.
To determine the probabilities of complements.
(13.6)Pg.961: 8-20