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Class 9 The Mathematics of Maybe: Introduction to Probability: cheat sheet
CBSE Mathematics. Probability measures how likely an event is, from 0 (impossible) to 1 (certain), by counting equally likely outcomes.
Key ideas
- Outcomes must be equally likely: each face of a fair die, each card of a well-shuffled deck.
- An impossible event has probability 0 and a sure event has probability 1.
- The probabilities of an event and its complement (not happening) add up to 1.
- A deck has 52 cards: 4 suits of 13 (hearts and diamonds red, spades and clubs black); 12 face cards (J, Q, K); 4 aces.
- Two dice give 6 × 6 = 36 outcomes; two coins give 4 (HH, HT, TH, TT).
- When cards or balls are removed, count again from what is left.
Remember
| Probability of an event | P(E) = favourable outcomes ÷ all outcomes |
| Range | 0 ≤ P(E) ≤ 1 |
| Complement | P(not E) = 1 − P(E) |
Watch out
- Counting aces as face cards (face cards are only J, Q and K).
- Taking 12 outcomes for two dice instead of 36.
- Not updating the total after cards are removed.
Worked example
All the spades are removed from a deck of 52 cards. One card is drawn from the rest. Find the probability that it is a face card.
Working: 39 cards are left, and 9 of them are face cards
Answer: 3/13
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