Skills we've learned. Skills we need. 7 3 Independent and Dependent Events. March 17, Alg2 Notes 7.3.notebook

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1 7 3 Independent and Dependent Events Skills we've learned 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? Skills we need 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 warm up Warm up Answers 7 12 Warm up ans. 1

2 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 = 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: 2. Geometric Probability: Experimental Probability: OR: = Area of Shaded:.5(2)(2) = 2 Area of Total: (4)(4) = 16 P(Shaded) = 2/16 = 1/8 300 coin flips, 120 tails. P(tails) = 120/300 = 2/5 Lesson 7.2 Summary 2

3 7 3 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. Learning Target 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 twice 2. draw a card twice 3. draw a name out of a hat 4. rolling 5 dice in Yahtzee 5. in three rolls, getting a Yahtzee Identifying Ind/Dep 3

4 II. Probability of Independent Events 6. Find the probability of getting three heads in a row when flipping a fair two sided coin. 7. Find the probability of drawing three face cards if between pulls you replace the card. Prob. of Independent Events 8. A six sided 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) You try 4

5 III. Probability of Dependent Events 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. The tree diagram shows the probabilities for choosing two pieces of fruit from a bag containing 2 lemons and 1 lime. Probability of Dependent Events 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. You try 5

6 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. You try Feb 15 12:14 PM 6

7 IV. Using Tables to Find Conditional Probability A. that an emigrant is from the West B. that someone selected from the South region is an immigrant C. that someone selected is an emigrant and is from the Midwest Using Tables V. Mixing it Up... In many cases involving random selection, events are independent when there is replacement and dependent when there is not replacement. A. selecting two hearts when the first card is replaced B. selecting two hearts when the first card is not replaced C. a queen is drawn, is not replaced, and then a king is drawn A. B. C. Mixing it up 7

8 7.3 p.503 #1 14, 17 23, 25 27, Homework 8