13 -5 Compound Events Warm Up Lesson Presentation

13 -5 Compound Events Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2 Holt Mc. Dougal Algebra 2

13 -5 Compound Events Warm Up 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. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Objectives Find the probability of mutually exclusive events. Find the probability of inclusive events. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Vocabulary simple event compound event mutually exclusive events inclusive events Holt Mc. Dougal Algebra 2

13 -5 Compound Events A simple event is an event that describes a single outcome. A compound event is an event made up of two or more simple events. Mutually exclusive events are events that cannot both occur in the same trial of an experiment. Rolling a 1 and rolling a 2 on the same roll of a number cube are mutually exclusive events. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Remember! Recall that the union symbol means “or. ” Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 1 A: Finding Probabilities of Mutually Exclusive Events A group of students is donating blood during a blood drive. A student has a having type O blood and a probability of having type A blood. Explain why the events “type O” and “type A” blood are mutually exclusive. A person can only have one blood type. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 1 B: Finding Probabilities of Mutually Exclusive Events A group of students is donating blood during a blood drive. A student has a having type O blood and a probability of having type A blood. What is the probability that a student has type O or type A blood? P(type O type A) = P(type O) + P(type A) Holt Mc. Dougal Algebra 2

13 -5 Compound Events Check It Out! Example 1 a 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. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Check It Out! Example 1 b 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. What is the probability that a student voted for Kline or Vila? P(Kline Vila) = P(Kline) + P(Vila) = 20% + 55% = 75% Holt Mc. Dougal Algebra 2

13 -5 Compound 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. Holt Mc. Dougal Algebra 2

13 -5 Compound Events 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. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Holt Mc. Dougal Algebra 2

13 -5 Compound Events Remember! Recall that the intersection symbol means “and. ” Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 2 A: Finding Probabilities of Compound Events Find the probability on a number cube. rolling a 4 or an even number P(4 or even) = P(4) + P(even) – P(4 and even) 4 is also an even number. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 2 B: Finding Probabilities of Compound Events Find the probability on a number cube. rolling an odd number or a number greater than 2 P(odd or >2) = P(odd) + P(>2) – P(odd and >2) There are 2 outcomes where the number is odd and greater than 2. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Check It Out! Example 2 a A card is drawn from a deck of 52. Find the probability of each. drawing a king or a heart P(king or heart) = P(king) + P(heart) – P(king and heart) Holt Mc. Dougal Algebra 2

13 -5 Compound Events Check It Out! Example 2 b A card is drawn from a deck of 52. Find the probability of each. drawing a red card (hearts or diamonds) or a face card (jack, queen, or king) P(red or face) = P(red) + P(face) – P(red and face) Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 3: Application 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? Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 3 Continued Step 1 Use a Venn diagram. Label as much information as you know. Being a senior and reading the paper are inclusive events. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 3 Continued Step 2 Find the number in the overlapping region. Subtract 215 from 630. This is the number of senior paper readers, 415. Step 3 Find the probability. P(senior reads paper) = P(senior) + P(reads paper) – P(senior reads paper) The probability that the student was a senior or read the daily paper is about 67. 6%. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 3 Continued Holt Mc. Dougal Algebra 2

13 -5 Compound Events Check It Out! Example 3 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? Holt Mc. Dougal Algebra 2

13 -5 Compound Events Check It Out! Example 3 Continued Step 1 Use a Venn diagram. Label as much information as you know. Having a hair styling and a manicure are inclusive events. 160 customers 63 33 28 hair styling Holt Mc. Dougal Algebra 2 manicure

13 -5 Compound Events Check It Out! Example 3 Continued Step 2 Find the number in the overlapping region. Subtract 28 from 61. This is the number of hair stylings and manicures, 33. Step 3 Find the probability. P(hair manicure) = P(hair) + P(manicure) – P(hair manicure) The probability that a customer had a hair styling or manicure is 77. 5%. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Recall from Lesson 11 -2 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. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 4 Application 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. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Example 4 Continued P(at least 2 students choose same) = 1 – 0. 0769 ≈ 0. 9231 The probability that at least 2 students choose the same butterfly is about 0. 9231, or 92. 31%. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Check It Out! Example 4 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. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Check It Out! Example 4 Continued P(at least 2 choose the same) 1 – 0. 8476 0. 1524 The probability that at least 2 customers buy the same style is about 0. 1524, or 15. 24%. Holt Mc. Dougal Algebra 2

13 -5 Compound Events Lesson Quiz: Part I You have a deck of 52 cards. 1. Explain why the events “choosing a club” and “choosing a heart” are mutually exclusive. A card can have only one suit. 2. What is the probability of choosing a club or a heart? Holt Mc. Dougal Algebra 2

13 -5 Compound Events Lesson Quiz: Part II The numbers 1– 9 are written on cards and placed in a bag. Find each probability. 3. choosing a multiple of 3 or an even number 4. choosing a multiple of 4 or an even number 5. Of 570 people, 365 were male and 368 had brown hair. Of those with brown hair, 108 were female. What is the probability that a person was male or had brown hair? Holt Mc. Dougal Algebra 2

13 -5 Compound Events Lesson Quiz: Part III 6. Each of 4 students randomly chooses a pen from 9 styles. What is the probability that at least 2 students choose the same style? 0. 5391 Holt Mc. Dougal Algebra 2