1. Five-Minute Check (over Lesson 12–6) Mathematical Practices 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
Lesson Menu

2. Determine whether the events are mutually exclusive.
rolling two number cubes and getting doubles or a sum of 11
A. mutually exclusive
B. not mutually exclusive
5-Minute Check 1

3. Determine whether the events are mutually exclusive.
rolling one number cube and getting a number greater than 4 or an odd number
A. mutually exclusive
B. not mutually exclusive
5-Minute Check 2

4. Using the table, find the probability that a girl who plays hockey will be chosen as the Athlete of the Year award. A. B. C. D.
5-Minute Check 1

5. Using the table, find the probability of choosing a boy or a soccer player as Athlete of the Year.
5-Minute Check 2

6. Using the table, find the probability of choosing a swimmer or hockey player as Athlete of the Year.
5-Minute Check 3

7. 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
5-Minute Check 1

8. 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
B. 0.25
C. 0.34 D
5-Minute Check 2

9. A. P(roll a 6): ; roll a number cube 75 times
Which of these experiments is most likely to have results that match the given theoretical probability?
A. P(roll a 6): ; roll a number cube 75 times
B. P(roll a 2 or 3): ; roll a number cube 15 times
C. P(roll an even number ): ; roll a number cube 20 times
D. P(roll a 4): ; roll a number cube 1 time __ 1 6 3 2
5-Minute Check 3

10. Mathematical Practices 2 Reason abstractly and quantitatively.
4 Model with mathematics.
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. MP

11. You found simple probabilities.
Find probabilities of independent and dependent events
Find probabilities of events given the occurrence of other events.
Then/Now

12. conditional probability probability tree
compound event
independent events
dependent events
conditional probability
probability tree
Vocabulary

13. Students who draw odd numbers will be on the Red team.
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?
Example 4

14. Let A be the event that an even number is drawn.
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.
Example 4

15. Draw a Venn diagram to represent this situation.
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.
Answer: B
Example 4

16. Mr. Riley’s class is traveling on a field trip for Science class
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.
Example 4

17. Concept

18. Conditional probability formula.
Using the Conditional Probability
Formula
At a fruit stand, 24% of the grape bags have red grapes, 15% have black grapes, and 3% have both red and black grapes. A customer selects a bag at random.
A. What is the probability that the bag contains red grapes, given that it contains black grapes?
P(red ∣ black) =
Conditional probability formula.
Example 2

19. Simplify. Answer: or 20% Using the Conditional Probability Formula
Example 2

20. Conditional probability formula.
Using the Conditional Probability
Formula
At a fruit stand, 24% of the grape bags have red grapes, 15% have black grapes, and 3% have both red and black grapes. A customer selects a bag at random.
B. What is the probability that the bag contains black grapes, given that it contains red grapes?
P(black ∣ red) =
Conditional probability formula.
Example 2

21. Simplify. Answer: or 12.5% Using the Conditional Probability Formula
Example 2

22. 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%
Example 2

23. Concept

24. Probability of independent events.
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?
P(A and B) = P(A) • P(B)
Probability of independent events.
= 0.63 • 0.63
P(A) = P(B) = 0.63 =
Multiply.
Example 3

25. P [not(A and B)] = 1 – P(A and B) Probability of a complement.
Identify and Use Probability Rules
P [not(A and B)] = 1 – P(A and B)
Probability of a complement.
= 1 –
Substitution. =
Subtract.
So, the probability that at least one student does not have a cat or a dog for a pet is about 60%.
Answer:
Example 3

26. 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.
Example 3

27. Concept