The Mathematics of Maybe: Introduction to Probability

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

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