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.