Bethany White

Dr. Bethany White (Statistician, University of Toronto) discusses the probability of tossing coins, and the relationships to Pascal’s Triangle, binomial power expansions, the Binomial Theorem, and weighted outcomes.

1. Tossing a coin twice

  • Let’s toss a coin to decide if we walk left or right.
  • If we toss the coin twice, where will we end up?
  • Which path is more likely?

2. Tossing a coin 5 times

  • Let’s toss a coin 5 times.
  • Which paths are we more likely to follow?
  • What does this have to do with Pascal’s Triangle?

3. All possible outcomes

  • Let’s look at all the possible outcomes.
  • What pattern do we notice?

4. Probability & algebra

  • There is a link between probability and algebra!
  • Imagine H and T as X and Y, and see a link between probability, algebra and Pascal’s Triangle.

5. Weighted outcomes

  • If you plot the frequency of one of two equally likely events as a graph, its plot looks like a “bell”.
  • If the events are not equally likely, the graph skews to one side of the other.