Download Events That Are Not Mutually Exclusive

Five-Minute Check (over Lesson 13–5)
CCSS
Then/Now
New Vocabulary
Example 1: Real-World Example: Identify Mutually Exclusive Events
Key Concept: Probability of Mutually Exclusive Events
Example 2: Real-World Example: Mutually Exclusive Events
Key Concept: Probability of Events That Are Not Mutually Exclusive
Example 3: Real-World Example: Events That Are Not Mutually Exclusive
Key Concept: Probability of the Complement of an Events
Example 4: Complementary Events
Concept Summary: Probability Rules
Example 5: Real-World Example: Identify and Use Probability Rules
Over Lesson 13–5
Determine whether the event is independent or
dependent. Samson ate a piece of fruit randomly
from a basket that contained apples, bananas,
and pears. Then Susan ate a second piece from
the basket.
A. independent
B. dependent
Over Lesson 13–5
Determine whether the event is independent or
dependent. Kimra received a passing score on
the mathematics portion of her state graduation
test. A week later, she received a passing score
on the reading portion of the test.
A. independent
B. dependent
Over Lesson 13–5
A spinner with 4 congruent sectors labeled 1–4 is
spun. Then a die is rolled. What is the probability
of getting even numbers on both events?
A. 1
B.
C.
D.
Over Lesson 13–5
Two representatives will be randomly chosen
from a class of 20 students. What is the
probability that Janet will be selected first and
Erica will be selected second?
A.
B.
C.
D.
Content Standards
S.CP.1 Describe events as subsets of a sample space (the
set of outcomes) using characteristics (or categories) of the
outcomes, or as unions, intersections, or complements of
other events (“or,” “and,” “not”).
S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) –
P(A and B), and interpret the answer in terms of the model.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
4 Model with mathematics.
You found probabilities of independent and
dependent events.
• Find probabilities of events that are mutually
exclusive and events that are not mutually
exclusive.
• Find probabilities of complements.
• mutually exclusive events
• complement
Identify Mutually Exclusive Events
A. CARDS Han draws one card from a standard
deck. Determine whether drawing an ace or a 9 is
mutually exclusive or not mutually exclusive.
Explain your reasoning.
Answer: These events are mutually exclusive. There
are no common outcomes. A card cannot be
both an ace and a 9.
Identify Mutually Exclusive Events
B. CARDS Han draws one card from a standard
deck. Determine whether drawing a king or a
club is mutually exclusive or not mutually
exclusive. Explain your reasoning.
Answer: These events are not mutually exclusive.
A king that is a club is an outcome that both
events have in common.
A. For a Halloween grab bag, Mrs. Roth has thrown
in 10 caramel candy bars, 15 peanut butter candy
bars, and 5 apples to have a healthy option.
Determine whether drawing a candy bar or an apple
is mutually exclusive or not mutually exclusive.
A. The events are mutually
exclusive.
B. The events are not
mutually exclusive.
B. For a Halloween grab bag, Mrs. Roth has thrown
in 10 caramel candy bars, 15 peanut butter candy
bars, and 5 apples to have a healthy option.
Determine whether drawing a candy bar or
something with caramel is mutually exclusive or
not mutually exclusive.
A. The events are mutually
exclusive.
B. The events are not
mutually exclusive.
Mutually Exclusive Events
COINS Trevor 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?
These events are mutually exclusive, since the coin
picked cannot be both a quarter or a penny.
Let Q represent picking a quarter.
Let P represent picking a penny.
There are a total of 30 + 25 + 40 + 15 or 110 coins.
Mutually Exclusive Events
P(Q or P) = P(Q) + P(P)
Probability of
mutually exclusive
events
Simplify.
Answer:
9
___
22
or about 41%
MARBLES Hideki collects colored marbles so he
can play with his friends. The local marble store
has a grab bag that has 15 red marbles, 20 blue
marbles, 3 yellow marbles and 5 mixed color
marbles. If he reaches into a grab bag and selects a
marble, what is the probability that he selects a red
or a mixed color marble?
A.
B.
C.
D.
Events That Are Not Mutually
Exclusive
ART Use the table below. What is the probability
that Namiko selects a watercolor or a landscape?
Since some of Namiko’s paintings are both
watercolors and landscapes, these events are not
mutually exclusive. Use the rule for two events that are
not mutually exclusive. The total number of paintings
from which to choose is 30.
Events That Are Not Mutually
Exclusive
Let W represent watercolors and L represent
landscapes.
Substitution
Simplify.
Answer: The probability that Namiko selects
a watercolor or a landscape is
or about 66%.
SPORTS Use the table.
What is the probability
that if a high school
athlete is selected at
random that the student
will be a sophomore or a
basketball player?
A.
B.
C.
D.
Complementary Events
GAMES Miguel bought 15 chances to pick the 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 Miguel will not
win the gift certificate?
Let event A represent selecting one of Miguel’s tickets.
Then find the probability of the complement of A.
Probability of a complement
Substitution
Subtract and simplify.
Complementary Events
Answer: The probability that one of Miguel’s tickets
will not be selected is
or about 93%.
RAFFLE At a carnival, Sergio bought 18 raffle
tickets, in order to win a gift certificate to the local
electronics store. If there is a total of 150 raffle
tickets sold, what is the probability Sergio will not
win the gift certificate?
A.
B.
C.
D.
Identify and Use Probability Rules
PETS A survey of Kingston High School
students found that 63% of the students had a
cat or a dog for a pet. If two students are chosen
at random from a group of 100 students, what is
the probability that at least one of them does not
have a cat or a dog for a pet?
Identify and Use Probability Rules
Understand
You know that 63% of the students have a cat or a dog
for a pet. The phrase at least one means one or more.
So you need to find the probability that either
• the first student chosen does not have a cat or a
dog for a pet or
• the second student chosen does not have a cat or
a dog for a pet or
• both students chosen do not have a cat or a dog
for a pet.
Identify and Use Probability Rules
Plan
The complement of the event described is that both
students have a cat or a dog for a pet. Find the
probability of this event, and then find the probability of
its complement.
Let event A represent choosing a student that does
have a cat or a dog for a pet.
Let event B represent choosing a student that does
have a cat or a dog for a pet, after the first student has
already been chosen.
These are two dependent events, since the outcome of
the first event affects the probability of the outcome of
the second event.
Identify and Use Probability Rules
Solve
Probability of
dependent events
Multiply.
Identify and Use Probability Rules
Probability of
complement
Substitution
Subtract.
Answer: So, the probability that at least one of the
students does not have a cat or a dog for a
pet is
or about 61%.
Identify and Use Probability Rules
Check
Use logical reasoning to check the reasonableness of
your answer.
The probability that one student chosen out of 100
does not have a cat or a dog for a pet is (100 – 63)%
or 37%. The probability that two people chosen out of
100 have a cat or a dog for a pet should be greater
than 37%. Since 61% > 37%, the answer is
reasonable.
PETS A survey of Lakewood High School students
found that 78% of the students preferred riding a
bicycle to riding in a car. If two students are chosen
at random from a group of 100 students, what is
the probability that at least one of them does not
prefer riding a bicycle to riding in a car?
A. 32%
B. 39%
C. 43%
D. 56%