Probability — Cheat Sheet

Class X · Mathematics Ch.14 · 8 Panels · Quick Reference

🎲 Basic Terms
Probability = a measure of chance
Always 0 ≤ P(E) ≤ 1
Vocabulary
TermMeaning
Experimentaction with uncertain result
Outcomeone possible result
Eventset of favourable outcomes
Trialone performance of the experiment
Elementary event: an event with exactly one outcome.
➗ Theoretical Probability
P(E) = (favourable outcomes) ÷ (total outcomes)
Condition: all outcomes must be equally likely (fair coin / unbiased die).
Sum rule: the probabilities of all elementary events add up to 1.
Never give a probability greater than 1 or less than 0 — recheck your counting.
🗂️ Sample Space (Total Outcomes)
ExperimentTotal outcomes
1 coin2
2 coins4
3 coins8 (2ⁿ)
1 die6
2 dice36 (6×6)
1 card from 5252
Counting rule: m outcomes then n outcomes = m × n total.
🔄 Complementary Events
P(not E) = 1 − P(E)
P(E) + P(Ē) = 1
Sure eventP = 1
Impossible eventP = 0
Shortcut: "at least one" problems are often easier as 1 − P(none).
🃏 Deck of 52 Cards
CategoryCount
Suits (♠♥♦♣)4 × 13 = 52
Red / Black26 / 26
Face cards (J,Q,K)12
Aces4
Cards per suit13
Hearts & Diamonds are red; Spades & Clubs are black.
⭐ All Formulas at a Glance
IdeaFormula
ProbabilityP(E) = fav / total
Range0 ≤ P(E) ≤ 1
ComplementP(Ē) = 1 − P(E)
Sure eventP = 1
Impossible eventP = 0
Sum of allΣP = 1
🎯 Two-Dice Sums
SumWaysProbability
2 or 1211/36
3 or 1122/36
766/36 = 1/6
Sums are NOT equally likely! 7 is the most probable sum; 2 and 12 the least.
Always count the 36 ordered pairs, e.g. (2,5) and (5,2) are different.
🧠 Exam Quick Recall
Method: (1) count total outcomes, (2) count favourable, (3) divide, (4) simplify the fraction.
Common mistakes: forgetting a card is removed (without replacement); assuming dice sums are equally likely; miscounting face cards (12, not 16).
Always simplify: 26/52 = 1/2. Leave the answer as a reduced fraction unless told otherwise.
Sanity check: a probability must land between 0 and 1.