EQ What are compound events Warm Up One

EQ: What are compound events? Warm Up One card is drawn from the deck. Find each probability. 1. selecting a two 2. selecting a face card

EQ: What are 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.

EQ: What are compound events? Remember! Recall that the union symbol means “or. ”

EQ: What are 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.

EQ: What are 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)

EQ: What are 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.

EQ: What are 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%

EQ: What are 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.

EQ: What are 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.

EQ: What are compound events?

EQ: What are compound events? Remember! Recall that the intersection symbol means “and. ”

EQ: What are 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.

EQ: What are 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.

EQ: What are 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)

EQ: What are 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)

EQ: What are 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?

EQ: What are 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.

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%.

Example 3 Continued

EQ: What are 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?

EQ: What are 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 manicure

EQ: What are 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%.

EQ: What are 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.

EQ: What are 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.

EQ: What are 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%.

EQ: What are 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.

EQ: What are 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%.

EQ: What are compound events?

EQ: What are 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?

EQ: What are 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?

EQ: What are 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