Skills we've learned
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Alg2 Notes 7.3.notebook February 15, 2013 Skills we need Skills we've learned 73 Independent and Dependent Events 1. In a box of 25 switches, 3 are defective. What is the probability of randomly selecting a switch that is not defective? 2. There are 12 E’s among the 100 tiles in Scrabble. What is the probability of selecting all 4 E’s when selecting 4 tiles? 4. There are 5 blue, 4 red, 1 yellow and 2 green beads in a bag. Find the probability that a bead chosen at random from the bag is: 1. Blue 2. Green 3. Blue or Green 4. Blue or Yellow 5. Not red 6. Not Yellow Warmup Answers 7 12
Transcript of Skills we've learned
Alg2 Notes 7.3.notebook February 15, 2013
Skills we need
Skills we've learned
73 Independent and Dependent Events
1. In a box of 25 switches, 3 are defective. What is the probability of randomly selecting a switch that is not defective?2. There are 12 E’s among the 100 tiles in Scrabble. What is the probability of selecting all 4 E’s when selecting 4 tiles?
4. There are 5 blue, 4 red, 1 yellow and 2 green beads in a bag. Find the probability that a bead chosen at random from the bag is:
1. Blue 2. Green 3. Blue or Green4. Blue or Yellow 5. Not red 6. Not Yellow
Warmup Answers
712
Alg2 Notes 7.3.notebook February 15, 2013
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 7.1 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 Notes 7.3.notebook February 15, 2013
73 Independent and Dependent Events
1. Determine whether events are independent or dependent.
2. Find the probability of independent and dependent events.
Political Analysts can use demographic information and probabilities to predict the results of elections.
I. Identifying Dependent/Independent
Events are independent events if the occurrence of one event does not affect the probability of the other.Events are dependent events if the occurrence of one event affects the probability of the other.
Identify:1. flip a coin twice2. draw a card twice3. draw a name out of a hat4. rolling 5 dice in Yahtzee 5. in three rolls, getting a Yahtzee
Alg2 Notes 7.3.notebook February 15, 2013
II. Probability of Independent Events
6. Find the probability of getting three heads in a row when flipping a fair twosided coin.
7. Find the probability of drawing three face cards if between pulls you replace the card.
8. A sixsided cube has four sides that are colored red, one side is white, and one side is yellow. Find the probability of tossing red, then white, then yellow.
The result of any toss does not affect the probability of any other outcome.
P(red, then white, and then yellow) = P(red) • P(white) • P(yellow)
Alg2 Notes 7.3.notebook February 15, 2013
III. Probability of Dependent Events
The tree diagram shows the probabilities for choosing two pieces of fruit from a bag containing 2 lemons and 1 lime.
To find the probability of dependent events, you can use conditional probability P(B|A), the probability of event B, given that event A has occurred.
9. Two cubes are rolled one white, and one yellow. Find the probability that the white cube shows a 6 and the sum of the two cubes is greater than 9.
Step 1. Determine the probability of each part.
Step 2 Find the probability.
Alg2 Notes 7.3.notebook February 15, 2013
10. Two cubes are rolled one white, and one yellow. Find the probability that the yellow cube shows an even number and the sum is 5.
Alg2 Notes 7.3.notebook February 15, 2013
IV. Using Tables to Find Conditional Probability
A. that an emigrant is from the WestB. that someone selected from the South region is an immigrant
C. that someone selected is an emigrant and is from the Midwest
In many cases involving random selection, events are independent when there is replacement and dependent when there is not replacement.
V. Mixing it Up...
A. selecting two hearts when the first card is replacedB. selecting two hearts when the first card is not replacedC. a queen is drawn, is not replaced, and then a king is drawn
A.
B.
C.
Alg2 Notes 7.3.notebook February 15, 2013
Due in Class:7.3 p.503 #1 14, 17 23, 25 27, 31, 32, 38
Have a fantastic 5day break!
