🌳 What is a Probability Tree Diagram?
A tree diagram is a picture that shows all possible outcomes of events happening one after another. Each branch represents one possible result.
At each branch, you write the probability of that outcome happening.
P(Event) = Number of favorable outcomesTotal number of possible outcomes
💡 Tip: The probabilities on all branches from the same point must always add up to 1!
📖 Example 1 — Skittles Problem
1 Max has 5 red and 3 orange Skittles (8 total). He eats one, then picks another.
2 First pick: P(Red) = 5/8, P(Orange) = 3/8
3 If first was Red (7 left: 4R, 3O): P(Red) = 4/7, P(Orange) = 3/7
4 If first was Orange (7 left: 5R, 2O): P(Red) = 5/7, P(Orange) = 2/7
✅ P(at least one Orange) = 1 − P(both Red) = 1 − (5/8 × 4/7) = 1 − 20/56 = 36/56 = 9/14
🔢 Fundamental Counting Principle (FCP)
If one event can happen in m ways and another can happen in n ways, then both events together can happen in m × n ways.
Total outcomes = n₁ × n₂ × n₃ × ... × nₖ
📖 Example 2 — Outfit Combinations
1 3 shirts, 4 pants, 2 shoes
2 Total outfits = 3 × 4 × 2 = 24 outfits
✅ Using FCP: multiply all the choices together!
🎯 Key Probability Rules
💡 Without replacement = total decreases each time!
💡 With replacement = total stays the same each time!
🎯 Choose Your Problems!
Select the problems you want to practice. You need at least 1!