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6/5/ C Sample Spaces

Example 1 While on vacation, Carlos can go snorkeling, boating, and paragliding. In how many ways can Carlos do the three activities? Make an organized list to show the sample space. Make an organized list. Use S for snorkeling, B for boating, and P for paragliding. There are 6 ways Carlos can do the three activities. SBPSPBBSPBPSPSBPBS

Example 2 A.8 B.12 C.16 D.24 Ken, Betsy, Sally, and David are seated in a row at the head table at a student council meeting. In how many ways can the four students be seated?

Example 3 A car can be purchased with either two doors or four doors. You may also choose leather, fabric, or vinyl seats. Use a tree diagram to find all the buying options. List each choice for the number of doors. Then pair each choice for the number of doors with each choice for the type of seats.

There are six possible buying options.

Example 4 A.3 B.5 C.6 D.8 A pair of sneakers can be purchased with either laces or Velcro. You may also choose white, gray, or black sneakers. Use a tree diagram to find how many different sneakers are possible.

Example 5 Chloe wants to buy a bouquet of flowers in a vase. The flower shop has roses, daffodils, and tulips and has four different vases from which to choose. Use the Fundamental Counting Principle to find the total number of possible outcomes of a bouquet made up of two types of flowers in a vase. number of outcomes for flower choice number of outcomes for vase choice total number of outcomes = 3 4 = 12 There are 12 different outcomes.

Example 6 A restaurant offers a pasta bar where customers can choose from fettuccine, linguine, and macaroni for their pasta choice, and three types of sauce. Use the Fundamental Counting Principle to find the total number of outcomes of a pasta dish with one type of pasta and one sauce. A.3 B.6 C.9 D.12

It’s Your Turn!

6/5/ A Probability of Simple Events

Probability- the chance that an event will occur Simple Event- one outcome or a collection of outcomes Random- if outcomes are equally likely to occur

Complementary events- two events in which either one or other must occur BUT cannot occur at the same time – heads or tails

Example 1 There are six equally likely outcomes on the spinner shown. Find the probability of landing on 1. There is one section of the spinner labeled 1.

Example 2 A number cube with sides labeled 1 through 6 is rolled. Find the probability of rolling a 4. A. B. C. D.

Example 3 There are six equally likely outcomes on the spinner shown. Find the probability of landing on 2 or 4. The word or indicates that the number of favorable outcomes needs to include the section labeled 2 and the section labeled 4. There is one section of the spinner labeled 2 and one section labeled 4.

Example 4 A number cube with sides labeled 1 through 6 is rolled. Find the probability of rolling a number greater than 3. A. B. C. D.

Example 5 Find Probability of the Complement There are six equally likely outcomes on the spinner shown. The spinner is spun once. Find the probability of not landing on 6. The probability of not landing on 6 and the probability of landing on 6 are complementary. So, the sum of the probabilities is 1.

Example 6 A number cube with sides labeled 1 through 6 is rolled. Find the probability of not rolling an even number. A. B. C. D.

Example 7 A sportscaster predicted that the Tigers had a 75% chance of winning tonight. Describe the complement of this event and find its probability. The complement of winning is not winning. The sum of the probabilities is 100%. Think 75% plus what number equals 100%? So, the probability that the Tigers will not win tonight is 25%.

Example 8 A.20% B.25% C.45% D.50% Celia guesses the probability that her parents will allow her to sleep over at her best friend’s house tonight is 55%. What is the probability that Celia will not be allowed to sleep over?

It’s Your Turn!

Homework Pg. 721 #1-22 Evens