Why It Matters: Probability and Counting Principles

According to the news, the lottery jackpot is climbing by the hour.  Long lines of dreamers are forming wherever lottery tickets are sold.  While you don’t usually buy lottery tickets, it is getting tempting.  Just imagine what you could do with $100 million dollars.  Perhaps you could retire early or never even go to work.  Maybe visit a beautiful island.  All you need to do is pick the correct numbers, and the jackpot is all yours.

Image shows numbered balls as would be used to select the winning numbers of a lottery.

 

It sounds easy enough; just six simple numbers.  But how likely are you to win?  And could you increase the likelihood of winning by purchasing more lottery tickets?

 

To answer these questions, you need to know about permutations and combinations.  So learn about them as you complete this module, and then we’ll return to the lottery at the end.  Then you’ll be able to decide whether you want to stand in line to purchase a ticket.

Photo shows blue ocean water in an inlet between rock structures.

 

Learning Objectives

Counting Principles

  • Solve counting problems using the Addition Principle and the Multiplication Principle.
  • Solve counting problems using permutations and combinations  involving n distinct objects.
  • Find the number of subsets of a given set.
  • Solve counting problems using permutations involving n non-distinct objects.
  • Apply the Binomial Theorem

Probability

  • Construct probability models.
  • Compute probabilities of equally likely outcomes.
  • Compute probabilities of the union of two events.
  • Use the complement rule to find probabilities.
  • Compute probability using counting theory.