Unit 6 Probability & Simulation: the Study of randomness Simulation Probability Models General Probability Rules

 the imitation of chance behavior, based on a model that accurately reflects the phenomenon under consideration, is called simulation.

Estimate the likelihood by actually observing the phenomenon many times Develop a probability model and calculate a theoretical answer Simulate multiple repetitions

1. State the problem or describe the random phenomenon 2. State the assumptions 1. Individual likeliness 2. Independent 3. Assign digits to represent outcomes 4. Simulate many repetitions 5. State your conclusions

 I have four children. How likely would it be to have a girl among my children?

1. State the problem or describe the random phenomenon 2. State the assumptions (individual likeliness, independent) 3. Assign digits to represent outcomes 4. Simulate many repetitions 5. State your conclusions

RandInt (0, 99, 10) RandInt (0, 9, 5) RandInt (0, 1, 10)

 Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. Probability is the long-run proportion of repetitions on which an event occurs.

 Count Buffon  in the 1700's  4040 times  2048 heads for Karl Pearson around ,000 times 12,012 heads for John Kerrich imprisoned in WWII 10,000 times 5067 heads for

 Thinking about Randomness  read pg 409

 What is the sample space when we roll two dice? What is the sample space when we record four coin tosses? Sometimes the sample space varies depending on what exactly you're asking for! What is the sample space when we toss a coin and roll a die?

What is the sample space when we record four coin tosses? What is the sample space when we toss a coin and roll a die? Being able to properly enumerate the outcomes in a sample space is critical to determining probabilities. Sometimes it's helpful to use a tree diagram.