Chapter 6 Review

1. Chapter 6 Review By: Hannah Ashmore, Caroline Hollar, and HaerinIm

2. Section 1: Vocab • Simulation: imitation of chance behavior based on a model that accurately reflects the phenomenon under consideration. • • Independent: The results of one trial have no influence on another trial.

3. Section 1: Key Points • We use a simulation to provide approximate answers to our questions when carrying out an experiment, sample survey, or observational survey is too costly, too slow or, practical. • • A probability model can be used to calculate a theoretical probability.

4. Section 1: Key Points cont. 1.State the problem or describe the random phenomenon 2.State the assumptions 3.Assign digits to represent outcomes 4.Simulate many repetitions (trials) 5.State your conclusions

5. Section 1: Example of Simulation 1.State the problem or describe the random phenomenon 2.State the assumptions 3.Assign digits to represent outcomes 4.Simulate many repetitions (trials) 5.State your conclusions 1. Toss a coin 10 times. What is the likelihood of a run with at least 3 consecutive heads or 3 consecutive tails? 2. Assumptions: Head and Tail are equally likely to occur. Tosses are independent from each other. 3. Odd digits: Heads. Even digits: Tails 4. Use table B and record all the numbers that are randomly selected and stop when you reach 3 consecutive heads or 3 consecutive tails. Repeat this step 3 times. 5. The probability is: The #of trials that result in 3 consecutive H or T ______________________________________ The total number of trials

6. Section 2: Vocab • Random: if individual outcomes are uncertain, but there is a regular distribution of outcomes in a large number of repetitions • Probability: the proportion of times the outcome would occur in a very long series of repetitions (long-term relative frequency) • Sample Space (S): set of all possible outcomes. • Event: Any outcome or set of outcomes of a random phenomenon (subset of the sample space). • Venn Diagram: Show events as disjoint or intersecting regions.

7. Section 2: Vocab cont. • Probability model: A mathematical description of a random phenomenon consisting of two parts; a sample space (S) and a way of assigning probabilities to events • Multiplication principle: if you can do one task in n1 number of ways and a second task in n2 number of ways then both tasks can be done by (n1 x n2). • Sampling with replacement: Objects selected from distinct choices be replaced before the next selection. Probabilities are the same for each draw. • Sampling without replacement: Probabilities change for each new selection. • Tree Diagram: begins with a point and draws a line to each possible outcome. The results look like a tree with branches and an outcome and a sample space is one of the paths through the tree. • Disjoint: (AKA Mutually Exclusive) means that they have no outcomes in common.

8. Section 2: Probability Rules • Any probability is a number between 0 and 1. • The sum of the probabilities of all possible outcomes must equal 1. • If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities. (Addition Rule) • The probability that an event does not occur is 1-the probability that the event does occur. (Compliment Rule)

9. Section 2: Example of Tree Diagram

10. Section 3: Vocab • Union: the event that at least one of the collection of events occurs. • Joint Event: the simultaneous occurrence of two events. • Conditional Probability: the probability of one event under the condition that we know another event. • Intersection: all of the events of a collection of events occur

11. Section 3: Example of Venn Diagram

12. Section 3: Examples Cont. • Probability WS