Transcript Glencoe Geometry - Burlington County Institute of Technology

Five-Minute Check (over Lesson 13–4)
CCSS
Then/Now
New Vocabulary
Example 1: Identify Independent and Dependent Events
Key Concept: Probability of Two Independent Events
Example 2: Real-World Example: Probability of Independent
Events
Key Concept: Probability of Two Dependent Events
Example 3: Probability of Dependent Events
Example 4: Standardized Test Example: Conditional
Probability
Key Concept: Conditional Probability
Over Lesson 13–4
An archer conducts a probability simulation to find
that he hits a bull’s eye 21 out of 25 times. What is
the probability that he does not hit a bull’s eye?
A. 0.14
B. 0.16
C. 0.18
D. 0.20
Over Lesson 13–4
The administrators at a high school use a random
number generator to simulate the probability of
randomly selecting one student. The results are
shown in the table. What is the probability of
selecting a freshman?
A. 0.059
B. 0.25
C. 0.34
D. 0.425
Over Lesson 13–4
Which of these experiments is most likely to
have results that match the given theoretical
probability?
1
__
A. P(roll a 6): 6 ; roll a number
cube 75 times
1
__
B. P(roll a 2 or 3): 3 ; roll a number
cube 15 times
1
__
C. P(roll an even number ): 2 ; roll
a number cube 20 times
1
D. P(roll a 4): __
; roll a number
6
cube 1 time
Content Standards
S.CP.2 Understand that two events A and B are independent if the
probability of A and B occurring together is the product of their
probabilities, and use this characterization to determine if they are
independent.
S.CP.3 Understand the conditional probability of A given B as
and interpret independence of A and B as saying that the conditional
probability of A given B is the same as the probability of A, and the
conditional probability of B given A is the same as the probability of B.
Mathematical Practices
2 Reason abstractly and quantitatively.
4 Model with mathematics.
,
You found simple probabilities.
• Find probabilities of independent and
dependent events
• Find probabilities of events given the
occurrence of other events.
• compound event
• independent events
• dependent events
• conditional probability
• probability tree
Identify Independent and Dependent Events
Determine whether the event is
independent or dependent.
Explain your reasoning.
A. A die is rolled, and then a
second die is rolled.
Answer: The two events are independent because
the first roll in no way changes the
probability of the second roll.
Identify Independent and Dependent Events
Determine whether the event is independent or
dependent. Explain your reasoning.
B. A card is selected from a deck of cards and
not put back. Then a second card is selected.
Answer: The two events are dependent because
the first card is removed and cannot be
selected again. This affects the probability
of the second draw because the sample
space is reduced by one card.
Determine whether the event is independent or
dependent. Explain your reasoning.
A. A marble is selected from a bag. It is not put
back. Then a second marble is selected.
A. independent
B. dependent
Determine whether the event is independent or
dependent. Explain your reasoning.
B. A marble is selected from a bag. Then a card
is selected from a deck of cards.
A. independent
B. dependent
Probability of Independent Events
EATING OUT Michelle and Christina are going
out to lunch. They put 5 green slips of paper and
6 red slips of paper into a bag. If a person draws a
green slip, they will order a hamburger. If they
draw a red slip, they will order pizza.
Suppose Michelle draws a slip. Not liking the
outcome, she puts it back and draws a second
time. What is the probability that on each draw
her slip is green?
These events are independent since Michelle replaced
the slip that she removed. Let G represent a green slip
and R represent a red slip.
Probability of Independent Events
Draw 1 Draw 2
Probability of
independent events
Answer: So, the probability that on each draw
Michelle’s slips were green is
LABS In Science class, students are drawing
marbles out of a bag to determine lab groups.
There are 4 red marbles, 6 green marbles, and 5
yellow marbles left in the bag. Jacinda draws a
marble, but not liking the outcome, she puts it back
and draws a second time. What is the probability
that each of her 2 draws gives her a red marble?
A. 12.2%
B. 10.5%
C. 9.3%
D. 7.1%
Probability of Dependent Events
EATING OUT Refer to Example 2. Recall that
there were 5 green slips of paper and 6 red slips
of paper in a bag. Suppose that Michelle draws a
slip and does not put it back. Then her friend
Christina draws a slip. What is the probability that
both friends draw a green slip?
These events are dependent since Michelle does not
replace the slip she removed. Let G represent a green
slip and R represent a red slip.
Probability of Dependent Events
Probability of
dependent events
After the first green
slip is chosen, 10
total slips remain,
and 4 of those are
green.
Simplify.
Answer: So, the probability that both friends draw
green slips is
or about 18%.
LABS In Science class, students are again drawing
marbles out of a bag to determine lab groups.
There are 4 red marbles, 6 green marbles, and
5 yellow marbles. This time Graham draws a
marble and does not put his marble back in the
bag. Then his friend Meena draws a marble. What
is the probability they both draw green marbles?
A.
B.
C.
D.
Conditional Probability
Mr. Monroe is organizing the gym class into two
teams for a game. The 20 students randomly
draw cards numbered with consecutive integers
from 1 to 20.
• Students who draw odd numbers will be on the
Red team.
• Students who draw even numbers will be on
the Blue team.
If Monica is on the Blue team, what is the
probability that she drew the number 10?
Conditional Probability
Read the Test Item
Since Monica is on the Blue team, she must have
drawn an even number. So you need to find the
probability that the number drawn was 10, given that
the number drawn was even. This is a conditional
problem.
Solve the Test Item
Let A be the event that an even number is drawn.
Let B be the event that the number drawn is 10.
Conditional Probability
Draw a Venn diagram to represent this situation.
There are ten even numbers in the sample space,
and only one out of these numbers is a 10. Therefore,
the P(B | A) =
The answer is B.
Mr. Riley’s class is traveling on a field trip for Science class.
There are two busses to take the students to a chemical
laboratory. To organize the trip, 32 students randomly draw
cards numbered with consecutive integers from 1 to 32.
• Students who draw odd numbers will be on the first bus.
• Students who draw even numbers will be on the second bus.
If Yael will ride the second bus, what is the probability that
she drew the number 18 or 22?
A.
B.
C.
D.