1. International Studies Charter School.
Mrs. Rivas
International Studies Charter School.
Bell Ringer
Simplify. Write your answer using whole numbers and variables. 2)
1) 2𝑤+12 46
𝒘+𝟔 𝟐𝟑
𝟏 𝟒
3) 5𝑢 5𝑢−3 ÷4
𝟓𝒖 𝟒 𝟓𝒖−𝟑
4) (−7 𝑡 3 −18 𝑡 2 +12𝑡)÷𝑡
−𝟕 𝒕 𝟐 −𝟏𝟖𝒕+𝟏𝟐

2. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Objective: To find To find the probability of the event A and B and the event A or B.
Dependent Events
Two events are dependent if the occurrence of one event affects the probability of the second event.
Example: You have a bag with red and blue marbles. You draw one marble at random, and then another without replacing the first.
The colors drawn are dependent events. A red marble on the first draw changes the probability for each color on the second draw.

3. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Objective: To find To find the probability of the event A and B and the event A or B.
Independent Events
When the outcome of one event does not affects the probability of a second event, the two events are independent.
Example: The result of two roll of a number cube are independent. Getting a five on the first roll does not change the probability of getting a five on the second roll.

4. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 1
Classifying Events
Are the outcomes of the first trial dependent or independent?
(A) Roll a number cube. Then Spin a spinner.
The two events do not affect each other.
They are independent.

5. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 1
Classifying Events
Are the outcomes of the first trial dependent or independent?
(B) Pick one flash card, then another one from the stack of 30 flash cards.
Picking the first card affects the outcome of picking the second card.
The events are dependent.

6. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Classifying Events
You select a coin at random from your pocket. You replace the coin and select again. Are your selections independent events? Explain.
Yes, your selections are independent events because the number of coins in your pocket is the same after the coin is replaced.

7. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
To find the probability of two events occurring together, you have to decide whether one event occurring affects the other event.
Multiply to find the probability that two independent events will both occur.

8. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 2
Finding the Probability of Independent Events
Picnic At a picnic there are 10 diet drinks and 5 regular drinks. There are also 8 bags of fat-free chips and 12 bags of regular chips. If you grab a drink and a bag of chips without looking, what is the probability that you get a diet drink and a fat-free chips.
Is it important that you don’t look?
Yes, probability is based on random events. It is not random if you look.

9. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 2
Finding the Probability of Independent Events
Picnic At a picnic there are 10 diet drinks and 5 regular drinks. There are also 8 bags of fat-free chips and 12 bags of regular chips. If you grab a drink and a bag of chips without looking, what is the probability that you get a diet drink and a fat-free chips.
Event A
Event B
A and B are independent events. Picking a drink has no effect on picking the chips.
𝑷 𝑨 𝒂𝒏𝒅 𝑩 =𝑷 𝑨 ∙𝑷 𝑩
= # 𝒅𝒊𝒆𝒕 𝒅𝒓𝒊𝒏𝒌𝒔 𝑻𝒐𝒕𝒂𝒍 𝒅𝒓𝒊𝒏𝒌𝒔 ∙ # 𝒇𝒂𝒕 𝒇𝒓𝒆𝒆 𝑪𝒉𝒊𝒑𝒔 𝑻𝒐𝒕𝒂𝒍 𝒄𝒉𝒊𝒑𝒔
= 𝟏𝟎 𝟏𝟓 ∙ 𝟖 𝟐𝟎
= 𝟒 𝟏𝟓
=𝟎.𝟐𝟔𝟔𝟔
≈𝟐𝟔.𝟕%

10. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Finding the Probability of Independent Events
Picnic At a picnic there are 10 diet drinks and 5 regular drinks. There are also 8 bags of fat-free chips and 12 bags of regular chips. If you grab a drink and a bag of chips without looking, what is the probability that you get a regular drink and a regular chips.

11. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Mutually Exclusive Events
When two events cannot happen at the same time.
Example: Rolling an even number and rolling a multiple of five on a standard number cube.

12. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 3
Mutually Exclusive Events
You roll an standard number cube. Are the events mutually exclusive? Explain.
(A) Rolling a 2 and a 3
You cannot roll a 2 and a 3 at the same time. The events are mutually exclusive.

13. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 3
Mutually Exclusive Events
You roll an standard number cube. Are the events mutually exclusive? Explain.
(B) Rolling an even number and a multiple of 3.
You can roll a 6 which is an even number and a multiple of 3. The events are NOT mutually exclusive.

14. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Mutually Exclusive Events
You roll an standard number cube. Are rolling an even number and rolling a prime number mutually exclusive? Explain.
NO. The event are NOT mutually exclusive since 2 is a prime and an even number.

15. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
If the events ARE mutually exclusive you add the probabilities.
𝑷 𝑨 𝒐𝒓 𝑩 =𝑷 𝑨 +𝑷(𝑩)

16. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 4
Finding Probability for Mutually Exclusive Events
Language At your high school, a student can take one foreign language each term. About 37% of the students take Spanish. About 15% of the students take French. What is the probability that a student chosen at random is taking Spanish or French?
ONE foreign language each term means that a students cannot take both Spanish and French. So the events are MUTUALLY EXCLUSIVE
What are they asking you to FIND?
P(Spanish or French)
What are they GIVING you?
1 foreign language each term
37% of the students take Spanish
15% of the students take French

17. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 4
Finding Probability for Mutually Exclusive Events
Language At your high school, a student can take one foreign language each term. About 37% of the students take Spanish. About 15% of the students take French. What is the probability that a student chosen at random is taking Spanish or French?
For mutually Exclusive events
𝑷 𝑨 𝒐𝒓 𝑩 =𝑷 𝑨 +𝑷(𝑩)
𝑷 𝑺𝒑𝒂𝒏𝒊𝒔𝒉 𝒐𝒓 𝑭𝒓𝒆𝒏𝒄𝒉 =𝑷 𝑺𝒑𝒂𝒏𝒊𝒔𝒉 +𝑷(𝑭𝒓𝒆𝒏𝒄𝒉)
=𝟎.𝟑𝟕+.𝟏𝟓
≈𝟎.𝟓𝟐
The probability that a student chosen at random is taking Spanish or French is about 0.52 or bout 52%

18. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Finding Probability for Mutually Exclusive Events
At your high school, a student can take one foreign language each term. About 37% of the students take Spanish. About 15% of the students take French. About 9% of the students take Italian. What is the probability that a student chosen at random is taking Spanish, French or Italian?

19. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
If the events ARE NOT mutually exclusive you need to subtract the probability of the common outcome to find P(a or B)
𝑷 𝑨 𝒐𝒓 𝑩 =𝑷 𝑨 +𝑷 𝑩 −𝑷(𝑨 𝒂𝒏𝒅 𝑩)

20. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 4
Finding Probability
Multiple Choice Suppose you reach into the dish and select a token at random. What is the probability that the token is round or green?
The events are not mutually exclusive because you can not chose a round or green token at the same time.

21. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Example 4
Finding Probability
Multiple Choice Suppose you reach into the dish and select a token at random. What is the probability that the token is round or green?
𝑷 𝑹𝒐𝒖𝒏𝒅 𝒐𝒓 𝑮𝒓𝒆𝒆𝒏 =𝑷 𝑹 +𝑷 𝑮 −𝑷(𝑹 𝒂𝒏𝒅 𝑮)
= 𝟓 𝟗 + 𝟑 𝟗 − 𝟐 𝟗
= 𝟖 𝟗 − 𝟐 𝟗
= 𝟔 𝟗
= 𝟐 𝟑
The probability of selecting a round or green token is 𝟔 𝟗 , or 𝟐 𝟑

22. International Studies Charter School. Probability of Multiple events
Mrs. Rivas
International Studies Charter School.
Algebra 2 Section 11-3
Probability of Multiple events
Finding Probability
Suppose you reach into the dish and select a token at random. What is the probability that the token is square or red?