Probability

The chance of an event as a number from 0 to 1, counted from equally likely outcomes: coins, dice, cards and balls.

Key ideas

Only use the formula when all the outcomes are equally likely.
Every probability is between 0 and 1: an impossible event has 0, a sure event has 1.
An event and its complement (not happening) add up to 1.
A deck has 52 cards: 4 suits of 13; 26 red and 26 black; 12 face cards (jack, queen, king) and 4 aces.
Two coins give 4 equally likely outcomes (HH, HT, TH, TT); two dice give 36.
List or count the outcomes carefully before dividing.

Probability of an event E	P(E) = favourable outcomes ÷ total outcomes
Complement	P(not E) = 1 − P(E)
Range	0 ≤ P(E) ≤ 1

Treating the sums of two dice (2 to 12) as equally likely: there are 36 outcomes, not 11.
Counting aces as face cards.
Counting HT and TH as one outcome.

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