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Chapter 6 Probability and Simulation

Chapter 6 Probability and Simulation. Mmm, peanut butter!!. The Study of Randomness. Questions involving chance. How likely is it to have a couple to have 2 or more boys in a family of 4 children?

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Chapter 6 Probability and Simulation

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  1. Chapter 6 Probability and Simulation Mmm, peanut butter!! The Study of Randomness

  2. Questions involving chance • How likely is it to have a couple to have 2 or more boys in a family of 4 children? • What are the chances of two or more people sharing the same birthday in a classroom of 30 students? • What is the probability of a professional athlete testing positive for drug use even if you haven’t used drugs.

  3. 3 ways to answer probability problems • Estimate the likelihood of a result by observing the phenomenon many times. • Develop a probability model and use it to calculate a theoretical answer. • Create a model that, in some way, reflects the truth of the phenomenon and imitate many repetitions of the event: Simulation

  4. State the problem or describe the random phenomenon. State the assumptions Assign digits to represent outcomes Simulate many repetitions 5. State your conclusion in context Flip a coin 10 times, how likely is a string of 3 or more heads? Heads/Tails equally likely Flips are independent 0 – 4 = head : 5 – 9 = tail Enter random digit table at line 101, read off 10 digits and count strings of 3 or more heads Compute relative frequency 5 components of a simulation pg 394

  5. Age Discrimination? An October 23rd article in the Seattle Times reported that “Safeco Insurance Company recently laid off 10 of its sales staff due to budget cuts. 6 of the 10 people fired were older than 55, while a large proportion of the younger sales staff—who are paid less—kept their jobs. The Bureau of Labor Statistics reports that 32% of all sales people in the last census were 55 or older” Is this evidence of age discrimination at Safeco Insurance?

  6. How likely is it for 6 of 10 people over 55 to be fired if the proportion of >55 is 32%? Assuming 32% of workers > 55 Assuming that the firing of one worker is independent of firing of other workers Worker > 55: 00 – 31 Worker ≤ 55: 32 – 99 Select 10 random digits 00-99, observe how often value 00-31 ≥ 6 Repeat many times Age discrimination? • State the problem or describe the random phenomenon. • State the assumptions • Assign digits to represent outcomes • Simulate many repetitions • 5. State your conclusion in context

  7. The moment you all have been waiting for!! HWK #60: Exercises 6.1, 6.4, 6.11

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