Expressions and Lotteries

Return to List of Lectures

Previous Lecture

• Questions?
• Lottery Calculations (Lesson 1)
  • Math background (“Multiplication Principle,” “Combinations,” and “Expected Value” videos)
    • Two deciding factors
      • With or without replacement
      • Does order matter?
    • Multiplication principle calculates all expected outcomes...
      • n choices to make, k₁ ways to make first, k₂ to make second, ....
        • Total = k₁ × k₂ × ...
      • Ordered (i.e., choosing a for the first choice and b for the second is different from choosing a for the second choice and b for the first)
      • Replacement (i.e., if a is an option for both the first and second choices, you can choose it for both)
    • Combinations ignore order, only count possible choices
      • Without replacement
      • Unordered
    • Expected value adds probabilities times values
  • Lottery exercise
    • Probability of winning grand prize w/ 1 ticket
      • 1 / number of possible tickets (i.e., number of combinations of numbers)
      • (pick 6 numbers from 59)
      • 1 / (59 C 6)
      • = 1 / nchoosek(...) in Matlab
      • Probability ends up being about 2e-8
    • Probability of second place
      • # ways of picking 5 of the winning 6 numbers
        • = 6 C 5
      • ...Times 53 ways of not matching the 6th number
      • ...Gives number of ways of making a 2nd-place ticket
      • Probability = # 2nd place tickets / total # of tickets
    • Algorithm coming from mathematical model
    • Finish this lesson and see me for grading by Friday
• Next
  • Vectors
  • Hand out lesson 2
  • Read Attway sections 2.1.1, and 2.2
  • Edinburgh video on “Variables and Simple Arrays” optional: http://www.see.ed.ac.uk/teaching/courses/matlab/unit01/variables-arrays.shtml

Next Lecture