Probability appears regularly in Decision Making. The maths is rarely hard; the challenge is choosing the right rule quickly. These four ideas cover most questions.
1. Count the outcomes
With two dice there are 6 × 6 = 36 equally likely outcomes. A total of 10 can happen three ways (4+6, 5+5 and 6+4), so the probability is 3 ÷ 36 = 1/12.
2. "And" means multiply
For independent events, multiply the probabilities. The chance of two heads when tossing two coins is ½ × ½ = ¼.
3. "Or" means add — if they cannot both happen
Rolling a 1 or a 2 on one die: 1/6 + 1/6 = 1/3. Only add when the outcomes cannot happen at the same time.
4. The one-minus trick
For "at least one" questions, find the chance of none instead. Tossing three coins, the chance of no heads is ½ × ½ × ½ = 1/8, so the chance of at least one head is 1 − 1/8 = 7/8.
Without replacement
When items are not put back, the second probability changes. Drawing two aces from a standard deck: 4/52 × 3/51 = 1/221.