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NAME DATE 12-4 PERIOD Study Guide and Intervention Probability and Probability Distributions Probability In probability, a desired outcome is called a success; any other outcome is called a failure. Probability of Success and Failure Example 1 If an event can succeed in s ways and fail in f ways, then the probabilities of success, P(S), and of failure, P(F), are as follows. π(π) = π π and π(πΉ) = π +π π +π When 3 coins are tossed, what is the probability that at least 2 are heads? You can use a tree diagram to find the sample space. First Coin Second Coin H H T H T T Third Possible Coin Outcomes H HHH T HHT H HTH T HTT H THH T THT H TTH T TTT Of the 8 possible outcomes, 4 have at least 2 heads. 4 1 So the probability of tossing at least 2 heads is or . 8 2 Example 2 What is the probability of picking 4 fiction books and 2 biographies from a best-seller list that consists of 12 fiction books and 6 biographies? The number of successes is 12C4 Ξ 6C2. The total number of selections, s + f, of 6 books is C(18, 6). 12C4 Ξ 6C2 P(4 fiction, 2 biography) = or about 0.40 18C6 The probability of selecting 4 fiction books and 2 biographies is about 40%. Exercises 1. PET SHOW A family has 3 dogs and 4 cats. Find the probability of each of the following if they select 2 pets at random to bring to a local pet show. a. P(2 cats) b. P(2 dogs) c. P(1 cat, 1 dog) 2. MUSIC Eduardoβs MP3 player has 10 blues songs and 5 rock songs (and no other music). Find the probability of each of the following if he plays six songs at random and songs maynot repeat. Round to the nearest tenth of a percent. a. P(6 blues songs) b. P(4 blues songs, 2 rock songs) c. P(2 blues songs, 4 rock songs) 3. CANDY One bag of candy contains 15 red candies, 10 yellow candies, and 6 green candies. Find the probability of each selection. a. picking a red candy b. not picking a yellow candy c. picking a green candy d. not picking a red candy Chapter 12 24 Glencoe Algebra 2 NAME DATE 12-4 Study Guide and Intervention PERIOD (continued) Probability and Probability Distributions Probability Distributions A random variable is a variable whose value is the numerical outcome of a random event. A probability distribution for a particular random variable is a function that maps the sample space to the probabilities of the outcomes in the sample space. Example Suppose two dice are rolled. The table and the relative-frequency histogram show the distribution of the absolute value of the difference of the numbers rolled. Use the graph to determine which outcome is the most likely. What is its probability? 0 1 2 3 4 5 probability 1 6 5 18 2 9 1 6 1 9 1 18 Numbers Showing on the Dice Probability Difference 5 The greatest probability in the graph is 18. The most likely outcome is a difference of 5 1 and its probability is . 5 18 2 9 1 6 1 9 1 18 0 18 0 1 2 3 Difference 4 5 Exercises 1. PROBABILITY Four coins are tossed. a. Complete the table below to show the probability distribution of the number of heads. Number of Heads 0 1 2 3 4 Probability 3 8 5 16 1 4 3 16 1 8 1 16 Heads in Coin Toss Lesson 12-4 Probability b. Create a relative-frequency histogram. 0 1 2 3 Heads 4 c. Find P (four heads). Chapter 12 25 Glencoe Algebra 2