Ever wondered why a 7 comes up so often in Ludo?
Roll two dice and add them. You'll get 7 far more often than 2 or 12. Is the game unfair? No — it's probability! Some totals can be made in many more ways than others. Let's see exactly how many.
Revision notes
Use outcome grids for two dice, and multiply probabilities for independent events.
Roll two dice and add them. You'll get 7 far more often than 2 or 12. Is the game unfair? No — it's probability! Some totals can be made in many more ways than others. Let's see exactly how many.
Probability = number of favourable outcomes ÷ total number of outcomes (when every outcome is equally likely).
It's always between 0 (impossible) and 1 (certain).
With two dice there are 6 × 6 = 36 equally likely outcomes. (1, 6) and (6, 1) are DIFFERENT outcomes — the dice are different.
🔑 Key idea: P(event) = favourable ÷ total
P(total = 8) with two dice
Step 1: Count all outcomes
6 × 6 = 36 equally likely outcomes
Step 2: Count the ways to make 8
5 ways
Step 3: Probability = favourable ÷ total
P = 536
Answer: 536
Two events are independent if one doesn't affect the other — like tossing a coin and rolling a die.
P(A and B) = P(A) × P(B).
For events that can't happen together (mutually exclusive): P(A or B) = P(A) + P(B).
🔑 Key idea: AND → multiply. OR (can't both happen) → add.
A coin and a die: P(head and a 6)
Step 1: Probability of each event
P(A) = 12
P(B) = 16
Step 2: Multiply for AND
P(A and B) = 12 × 16 = 112
Why? The two events don't affect each other, so we multiply.
Answer: 112
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.