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Probability

This comprehensive guide covers the concept of probability, focusing on the Law of Large Numbers and its application in observational probabilities. Using the example of tossing piglets and dice, the relationship between the number of trials and the accuracy of observed outcomes is explained. The guide also illustrates how to calculate probabilities for different outcomes, showing how experimental results converge on theoretical probabilities as sample sizes increase. Engage in practical activities to reinforce understanding and application of probability.

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Probability

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  1. Probability Finding a probability using the law of large numbers.

  2. Day Light % Red Lights Probability 1 Red (1/1) 100 1.0 2 Green (1/2) 50 0.5 3 Red (2/3) 66.7 0.667 4 Red (3/4) 75 0.75 5 Green (3/5) 60 0.6 6 Green (3/6) 50 0.5 Observational Probability Determining the probability by what you see happens: As you increase the number of trials the Observational Probability gets closer to the actual probability.

  3. 100 100 90 80 70 60 50 40 30 Percent of Red 20 10 0 0 1 2 3 4 5 6 6 # of Outcomes

  4. 100 100 90 80 70 60 50 40 30 Percent of Red 20 10 0 0 1 2 3 4 5 6 6 # of Outcomes The graph, over time, settles down to 35% or we say P(red) = 0.35 Called “Law of Large Numbers”

  5. Pass the Pigs Outcomes: a) What are the possible outcomes for your piglet? Left Sider: Right Sider: Razorback: Trotter: Snouter:

  6. Pass the Pigs P(Outcomes): b) Toss your piglet 40 times, record how many times it lands in each position. Left Sider: Right Sider: Razorback: Trotter: Snouter: 40 40 40 40 40

  7. Pass the Pigs P(Outcomes from team): d) Combine your tosses with your teams. Left Sider: Right Sider: Razorback: Trotter: Snouter: Add up Total #

  8. Pass the Pigs P(Outcomes from Class): f) Combine your team tosses with the class. Left Sider: Right Sider: Razorback: Trotter: Snouter: Add up Total #

  9. Pass the Pigs If we created a spinner with the same probabilities, as the outcomes of tossing the piglets, what would it look like? A B Or more like Pg 3.1 on calculator

  10. Pass the Pigs h) Find P(Left or Right sider): • i) Find P(razor back or trotter): • j) Find P(razor back or left sider) • k) Find P(razor back or right sider or snouter) • l) Find P(not a left) Pg 3.2 for h,i,j Pg 3.3 for k,l

  11. Dice Project This project is worth 60 points and will be counted as a test. There will be no late dice projects accepted. Due date is Tuesday April 30A-day or May 1st B-day 2013 Your dice will be graded on the following: 1) Creativity (15 points): 2) Appearance (15 points): 3) Ease of use (10 points): {You will be tossing yours at least 40 times} 4) Test of fairness (20 points)? See examples of unique dice on next slide

  12. Unique Dice

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