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Name: _______________________ Date: __________ Intro to Probability! Example 1: A fair die is thrown. What is the probability of obtaining: a) a five? b) an even number? Example 2: A bag contains 4 black balls and 6 white balls. A ball is chosen from the bag at random. What is the probability of choosing a white ball? Example 3: Our class contains ___ people: ___ with blue eyes, ___ with green eyes, ___ with brown eyes, and ___ with other colors. The probability of selecting a person at random with brown eyes is: Example 4: When a batch of 145 paper clips were dropped onto 6 cm by 6 cm squared paper it was observed that 113 fell completely inside squares and 32 finished up on the grid lines. Find, to 2 decimal places, the estimated probability of a clip falling a) inside a square ______ b) on a line______ Terms to Know! 1. The number of ______________ is the total number of times the experiment is repeated. 2. The _________________ are the different results possible for one trial of the experiment. 3. The _________________ of a particular outcome is the number of times that this outcome is observed. 4. The list of all possible outcomes is called the _________________________. 5. The outcome, or set of outcomes, in whose probability we are interested is called a(n) ______________. 6. A selection is _______________ if each item to be selected is equally likely to be chosen. 7. The _____________________________ of an outcome is the frequency of that outcome expressed as a fraction or percentage of the total number of trials. Example Sample Space (list all possible outcomes) 1 Event Probability 2 3 4 *Can you develop a formula for finding the probability of an event A? ________________________ HW p. 372-373 #1-3, 15 In the diagram below, ____ represents __________ _____________, and the oval represents the __________ ___. n(A) = _____________________________________ n(U) = _____________________________________ P(A) = _____________________________________ P(A) = Sooooo… The probability of A = _____________________________________________ Ways to Find Sample Space: Before, we only talked about rolling one die, but what if you roll two, three? It’s best to make an organized list or a table. Example 5: Two fair dice are thrown. Find the probability that the total of the scores on the two dice is six. First, list the possible outcomes (i.e. the ________________________). How many will there be? _______ . There are two possible ways to do this: 1. List the possible outcomes. 2. Table ___________________ 1 2 3 4 5 6 1 2 3 4 5 6 Let A be the event that the total score is six. What are the possible ways to get a total score of six? ____________________________ n(A) = ________ and n(U) = _________ so P(A) = _____ Example 6: Illustrate the possible outcomes when 2 coins are tossed. 1. 2-D Grid 2. Tree Diagram You do: 1. Again two fair dice are thrown. What is the probability of getting a total score of 11? 2. The table shows the number of seeds in a seed pod of a sample of 100 plants of a specific species. Seeds per pod 10 11 12 13 14 15 16 17 18 Number of pods 2 21 24 19 11 8 4 3 8 Find the probability that a seed pod selected at random from the samples contains: (a) 14 seeds (b) more than 14 seeds