alg2 7.5b notes on monday.notebook · 2015. 3. 23. · alg2 7.5b notes on monday.notebook 1 march...
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Alg2 7.5B Notes on Monday.notebook
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March 23, 2015
warmup
75 Compound Events
One card is drawn from the deck. Find each probability.1. selecting a two 2. selecting a face card
Two cards are drawn from the deck. Find each probability.
3. selecting two kings when the first card is replaced.
4. selecting two hearts when the first card is not replaced.
• At a juicebottling factory, qualitycontrol technicians randomly select bottles and mark them pass or fail. The manager randomly selects the results of 50 tests and organizes the data by shift and result. The table below shows these results.
1) Find the probability that a bottle was inspected in the afternoon given that it failed the inspection. 2) Use conditional probabilities to determine on which shift a bottle is most likely to pass inspection.
Warmup answers
Alg2 7.5B Notes on Monday.notebook
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March 23, 2015
Lesson 7.1 Summary
Lesson 7.1 Summary:Three types of counting.1. The "options" counting2. The subset grouping where order matters3. 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 = 242. Order matters: out of three students, choosing a room rep and alternate.
A,B,C: AB, BA, BC, CB, AC, CA = 6 ways
A,B,C: AB, BA, BC, CB, AC, CA = 3 ways
3. Order doesn't matter: out of three students, choosing a partner for a quiz.
Lesson 7.2 Summary
Lesson 7.2 SummaryThree Types of Probability1. Theoretical Probability2. Geometric Probability3. 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 2552 51 102=
2. Geometric Probability:
2
2
2 2
4
4Area of Shaded: .5(2)(2) = 2Area of Total: (4)(4) = 16P(Shaded) = 2/16 = 1/8
3. Experimental Probability:
300 coin flips, 120 tails.P(tails) = 120/300 = 2/5
Alg2 7.5B Notes on Monday.notebook
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March 23, 2015
Lesson 7.3 Summary
Lesson 7.3 Summary:Independent and Dependent Events
1. Independent Event
2. Dependent Eventwhere means the probability of B, given that A has occurred.
A fair coin flipped 3 times, P(all tails) = (1/2)(1/2)(1/2) = 1/8
A diamond drawn, then a heart,P(diamond and heart) = (13/52)(13/51) = 169/2652 = 13/204
Lesson 7.4 Summary
Lesson 7.4 Summary:TwoWay Tables
1. Picking a random person
2. Picking a random person given another event
3. Doing this with joint relative frequencies and marginal relative frequencies
Alg2 7.5B Notes on Monday.notebook
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March 23, 2015
Types of Events
Types of EventsSimple Event an event that describes a single outcome
Compound Event an event made up of two or more simple events
Mutually Exclusive Events event that canot both occur in the same trial of an experiment.
Inclusive Events events that have one or more outcomes in common
Mutually Exclusive Events
Mutually Exclusive Events Continued
The probability of two mutually exclusive events occurring is equal to the sum of their individual probabilities.
1. What is the probability of drawing a heart or a club?you could do... P(heart) + P(club)
Alg2 7.5B Notes on Monday.notebook
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March 23, 2015
Inclusive Events
Inclusive Events
Inclusive events are events that have one or more outcomes in common. When you roll a number cube, the outcomes “rolling an even number” and “rolling a prime number” are not mutually exclusive. The number 2 is both prime and even, so the events are inclusive.
There are 3 ways to roll an even number, {2, 4, 6}.
There are 3 ways to roll a prime number, {2, 3, 5}.
The outcome “2” is counted twice when outcomes are added (3 + 3) . The actual number of ways to roll an even number or a prime is 3 + 3 – 1 = 5. The concept of subtracting the outcomes that are counted twice leads to the following probability formula.
P(A∪B) = P(A) + P(B) P(A∩B)
you try
P(A B) = P(A) + P(B) P(A∩B)
Find the probability on a number cube.rolling a 4 or an even number
rolling an odd number or a number greater than 2
Alg2 7.5B Notes on Monday.notebook
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March 23, 2015
You Try
A card is drawn from a deck of 52. Find the probability of each.drawing a king or a heart
drawing a red card (hearts or diamonds) or a face card (jack, queen, or king)
PAVenn
Practical Application ~ Venn
Of 1560 students surveyed, 840 were seniors and 630 read a daily paper. The rest of the students were juniors. Only 215 of the paper readers were juniors. What is the probability that a student was a senior or read a daily paper?
Step 1make a Venn Diagram
Alg2 7.5B Notes on Monday.notebook
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March 23, 2015
You Try PAVenn
Of 160 beauty spa customers, 96 had a hair styling and 61 had a manicure. There were 28 customers who had only a manicure. What is the probability that a customer had a hair styling or a manicure?
using the complement
Recall that the complement of an event with probability p, all outcomes that are not in the event, has a probability of 1 – p. You can use the complement to find the probability of a compound event.
Each of 6 students randomly chooses a butterfly from a list of 8 types. What is the probability that at least 2 students choose the same butterfly?
P(at least 2 students choose same) = 1 – P(all choose different)Use the complement.
Using the Complement
Alg2 7.5B Notes on Monday.notebook
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March 23, 2015
You Try PAPerm
In one day, 5 different customers bought earrings from the same jewelry store. The store offers 62 different styles. Find the probability that at least 2 customers bought the same style.
P(two customers bought same earrings) = 1 – P(all choose different)Use the complement.
Homework
7.5 p.522 #1, 6 11, 14 19, 26, 31 33
Test Thursday/Friday mostly multiple choice