Welcome to Probability.
This week is probability — the math of uncertainty. By Sunday you'll be fluent in the probability ratio (favorable / total), the fundamental counting principle that powers every "how many possible outcomes" question, permutations vs combinations (does order matter?), and the expected value machine that puts a fair price on any game of chance.
Topic 6 is the second half of the data side of the course. Topic 5 was descriptive — how to read a data set you already have. Topic 6 is predictive — what to expect from a process whose outcome isn't decided yet. The Major Assignment 3 anchor stitches these tools together on a real-world probability scenario.
By the end of this week, you'll be able to:
- Compare, compute and interpret theoretical and empirical probabilities.
- Develop and use the fundamental counting principle.
- Develop a procedure for finding expected value.
- Compute and interpret expected values.
Four phases, in order. Don't skip ahead — each one sets up the next.
- L01 · Simple probability.
- L02 · Fundamental counting principle.
- L03 · Sample spaces and the addition rule.
- L04 · Permutations and combinations.
- L05 · Expected value.
- L06 · Theoretical vs experimental probability.
- DQ 1 · Autofill a 1,000-row and a 4,000-row simulation column, Compute empirical probability with a locked-denominator formula, Compute theoretical probability for a fair n-sided die, Compare average deviation across two sample sizes (Law of Large Numbers)
- DQ 2 · Decide permutation vs combination on six game scenarios, Compute sample-space size with =PERMUT and =COMBIN, Compute probability via favorable / total, Convert probability to "1 to X" odds against winning
- Component 1 · Analysis
- Component 2 · Visualization
- Q1 · Probability involving one die or choosing from n distinct objects
- Q2 · Counting principle
- Q3 · Probability of selecting one card from a standard deck
- Q4 · Permutations and combinations: Problem type 2
- Q5 · Computing expected value in a game of chance
- Q6 · Experimental and theoretical probability for compound events
Plan for the whole week. These are typical times, not maximums — go faster if it clicks, slower if you're getting stuck.
You won't get through every lesson on the first try. Here's where to look:
Ready to start?
▸ Start Lesson 01