7 5 Compound Events. March 23, Alg2 7.5B Notes on Monday.notebook

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1 7 5 Compound Events At a juice bottling factory, quality control 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. 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. warm up Warm up answers 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 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 Lesson 7.4 Summary: Two Way 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 Lesson 7.4 Summary 3

4 Types of Events Simple 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 Types of 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) Mutually Exclusive Events 4

5 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 = 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) Inclusive Events 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 you try 5

6 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) You Try 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 1 make a Venn Diagram PA Venn 6

7 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? You Try PA Venn 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 7

8 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. You Try PA Perm 7.5 p.522 #1, 6 11, 14 19, 26, Test Thursday/Friday mostly multiple choice Homework 8