Alg2 Notes 7.4 and 7.5A Notes.notebook
March 19, 2015
7­4 Two­Way Tables
Skills we've learned
1. Find the probability of rolling a number greater than 2 and then rolling a multiple of 3 when a number cube is rolled twice. 2. A drawer contains 8 blue socks, 8 black socks, and 4 white socks. Socks are picked at random. Find the probability of picking a blue sock and then another blue sock. 3. Two cards are drawn from a deck of 52. Find the probability of
A. Selecting two face cards when the first card is replaced
B. Selecting two face cards when the first card is not replaced.
Skills we need
4. A bag contains 4 red and 2 yellow marbles. A marble is selected, kept out of the bag, and another marble is selected. Find each conditional probability of selecting the second marble.
A. P(red red) C. P(yellow yellow) B. P(red yellow)
D. P(yellow red)
warm­up
Warm­up Answers
1. Find the probability of rolling a number greater than 2 and then rolling a multiple of 3 when a number cube is rolled twice. 2/9
2. A drawer contains 8 blue socks, 8 black socks, and 4 white socks. Socks are picked at random. Find the probability of picking a blue sock and then another blue sock. 14/95
3. Two cards are drawn from a deck of 52. Find the probability of
A. selecting two face cards when the first card is replaced 9/169
B. selecting two face cards when the first card is not replaced 11/221
4. A bag contains 4 red and 2 yellow marbles. A marble is selected, kept out of the bag, and another marble is selected. Find each conditional probability of selecting the second marble.
Warm­up ans.
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Alg2 Notes 7.4 and 7.5A Notes.notebook
March 19, 2015
Lesson 7.1 Summary:
Three types of counting.
1. The "options" counting
2. The subset grouping where order matters
3. The subset grouping where order doesn't matter
1. Options: building a sundae, three choices of flavors, 4 choices of toppings, yes or no to nuts.
3 x 4 x 2 = 24
2. Order matters: out of three students, choosing a room rep and alternate.
A,B,C: AB, BA, BC, CB, AC, CA = 6 ways
3. Order doesn't matter: out of three students, choosing a partner for a quiz.
A,B,C: AB, BA, BC, CB, AC, CA = 3 ways
Lesson 7.1 Summary
Lesson 7.2 Summary
Three Types of Probability
1. Theoretical Probability
2. Geometric Probability
3. Experimental Probability
1. Theoretic Probability: Probability of choosing a red card: 26/52 = 1/2
Probability of choosing two red cards: order does not matter:
OR: 26 25 25
=
52 51 102
2. Geometric Probability:
4
2
4
2
2
Area of Shaded: .5(2)(2) = 2
Area of Total: (4)(4) = 16
P(Shaded) = 2/16 = 1/8
2
3. Experimental Probability:
300 coin flips, 120 tails.
P(tails) = 120/300 = 2/5
Lesson 7.2 Summary
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Alg2 Notes 7.4 and 7.5A Notes.notebook
March 19, 2015
Lesson 7.3 Summary:
Independent and Dependent Events
1. Independent Event A fair coin flipped 3 times, P(all tails) = (1/2)(1/2)(1/2) = 1/8 2. Dependent Event
where means the probability of B, given that A has occurred. A diamond drawn, then a heart,
P(diamond and heart) = (13/52)(13/51) = 169/2652 = 13/204
Lesson 7.3 Summary
7­4 Two­Way Tables
1. Construct and interpret two­way frequency tables of data when two categories are associated with each object being classified. Actually, what we are doing is learning what a two­way table is, then not doing it.
Recognizing and using data organized in joint and marginal relative frequencies Learning Target
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Alg2 Notes 7.4 and 7.5A Notes.notebook
March 19, 2015
7­3's way of using a Table
1) Suppose you asked 20 children and adults whether they liked broccoli. The table shows one way to arrange the data:
a) What is the probability that a person chosen randomly is a child that likes broccoli?
b) What is the probability that a person that likes broccoli is a child? *Conditional probability
7.3 way of tables
7­4's way of using a Table
1) Suppose you asked 20 children and adults whether they liked broccoli. The table shows one way to arrange the data:
The joint relative frequencies are the values in each category divided by the total number of values, shown by the shaded cells in the table. Each value is divided by 20, the total number of individuals.
The marginal relative frequencies are found by adding the joint relative frequencies in each row and column.
a) What is the probability that a person chosen randomly is a child that likes broccoli?
b) What is the probability that a person that likes broccoli is a child? *Conditional probability
7.4 way of tables
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Alg2 Notes 7.4 and 7.5A Notes.notebook
March 19, 2015
7­3 method again
2. A reporter asked 150 voters if they plan to vote in favor of a new library and a new arena. The table shows the results.
a) What is the probability that a voter will vote yes to the new library?
b) If you are given that a voter plans to vote no to the new library, what is the probability the voter also plans to say no to the new arena?
7.3 way of conditional relative frequency
7­4 method again
To find a conditional relative frequency , divide the joint relative frequency by the marginal relative frequency. Conditional relative frequencies can be used to find conditional probabilities.
2. A reporter asked 150 voters if they plan to vote in favor of a new library and a new arena. The table shows the results.
First: Make a table of the joint and marginal relative frequencies.
a) What is the probability that a voter will vote yes to the new library?
b) If you are given that a voter plans to vote no to the new library, what is the probability the voter also plans to say no to the new arena?
Conditional Relative Frequency
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Alg2 Notes 7.4 and 7.5A Notes.notebook
March 19, 2015
7­5A Compound Events if mutually exclusive
Find the probability of mutually exclusive events.
Finding the probability of a Yatzee in three rolls
7.5A Compound of exclusive
Mutually Exclusive Events
The probability of two mutually exclusive events occurring is equal to the sum of their individual probabilities.
P(A ∪ B) = P(A) + P(B)
1. What is the probability, when a number cube is rolled, of rolling less than a 3?
P(1 or 2) = P(1) + P(2) = 1/6 +1/6 = 1/3
Mutually exclusive
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Alg2 Notes 7.4 and 7.5A Notes.notebook
March 19, 2015
Mutually Exclusive Events
2. A group of students is donating blood during a blood drive. 9
A student has a probability of having type O blood and 20
2
a probability of having type A blood.
5
Explain why the events “type O” and “type A” blood are mutually exclusive.
A person can only have one blood type
What is the probability that a student has type O or type A blood?
Ex. 2
3. Each student cast one vote for senior class president. Of the students, 25% voted for Hunt, 20% for Kline, and 55% for Vila. A student from the senior class is selected at random.
Explain why the events “voted for Hunt,” “voted for Kline,” and “voted for Vila” are mutually exclusive.
Each student can vote only once
What is the probability that a student voted for Kline or Vila?
Ex. 3
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Alg2 Notes 7.4 and 7.5A Notes.notebook
March 19, 2015
7.4 p.514 #5, 15
7.5 p.522 #2­4, 12, 13
Quiz Quiz Quiz!! Group, Graphing Calc OK
Homework
Mar 19­11:11 AM
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