# Simulate many repetitions trials 5 state your

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Simulate many repetitions (trials) 5. State your conclusions Example 1: Suppose you left your statistics textbook and calculator in you locker, and you need to simulate a random phenomenon (drawing a heart from a 52-card deck) that has a 25% chance of a desired outcome. You discover two nickels in your pocket that are left over from your lunch money. Describe how you could use the two coins to set up you simulation. Example 2: Suppose that 84% of a university’s students favor abolishing evening exams. You ask 10 students chosen at random. What is the likelihood that all 10 favor abolishing evening exams? Describe how you could use the random digit table to simulate the 10 randomly selected students. Example 3: Use your calculator to repeat example 2 Homework: pg 397 6-1, 4, 5, 8, 15

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Chapter 6: Probability and Simulation: The Study of Randomness Section 6.2: Probability Models Knowledge Objectives: Students will: Explain what is meant by random phenomenon . Explain what it means to say that the idea of probability is empirical . Define probability in terms of relative frequency . Define sample space . Define event . Explain what is meant by a probability model . List the four rules that must be true for any assignment of probabilities. Explain what is meant by equally likely outcomes . Define what it means for two events to be independent . Give the multiplication rule for independent events . Construction Objectives: Students will be able to: Explain how the behavior of a chance event differs in the short- and long-run. Construct a tree diagram . Use the multiplication principle to determine the number of outcomes in a sample space. Explain what is meant by sampling with replacement and sampling without replacement . Explain what is meant by { A B } and { A B }. Explain what is meant by each of the regions in a Venn diagram . Give an example of two events A and B where A B = . Use a Venn diagram to illustrate the intersection of two events A and B . Compute the probability of an event given the probabilities of the outcomes that make up the event. Compute the probability of an event in the special case of equally likely outcomes . Given two events, determine if they are independent. Vocabulary: Empirical – based on observations rather than theorizing Random – individuals outcomes are uncertain Probability – long-term relative frequency Tree Diagram – allows proper enumeration of all outcomes in a sample space Sampling with replacement – samples from a solution set and puts the selected item back in before the next draw Sampling without replacement – samples from a solution set and does not put the selected item back Union – the set of all outcomes in both subsets combined (symbol: ) Empty event – an event with no outcomes in it (symbol: ) Intersect – the set of all in only both subsets (symbol: ) Venn diagram – a rectangle with solution sets displayed within Independent – knowing that one thing event has occurred does not change the probability that the other occurs
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