The meaning of probability From the preliminary course: An outcome is a result of an experiment or game. Eg rolling a 4 on a die. The sample space is the set of all possible outcomes. Eg 1, 2, 3, 4, 5 & 6 on a die. An event is a group of one or more outcomes. Eg rolling a prime number on a die. The theoretical probability of an event is given by: The probability of an event lies between 0 and 1. 0 ≤ P(E) ≤ 1 Two events are complementary if their probability adds to 1. P(Ē) is used for the complementary event to P(E). P(Ē) = 1 − P(E)

The meaning of probability A standard deck of cards contains: 52 cards (no joker). 2 colours, red & black, 26 in each. 4 suits, spades (black), clubs (black), diamonds (red) & hearts (red). Each suit has a 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King & Ace. The Jack, Queen & King are called picture cards. In the alphabet a, e, i, o & u are vowels. The other letters are consonants. If an experiment is carried out the results may be different to theory. This is called the experimental probability. This may also be called the relative frequency.

Example 1 Example 2 A card is drawn from a standard deck of cards. What is the probability of drawing a: king? black queen? P(K) = P(black queen) = Example 2 A bottle contains 12 red, 34 green, 46 blue and 78 yellow M & M’s. What is the probability of : drawing a green M & M? not drawing a green M & M? P(G) = P(not G) =

Example 3 Sharon rolls a die 60 times. The results were: 10 1’s, 8 2’s, 15 3’s, 11 4’s, 7 5’s & 9 6’s. What is the probability of rolling a: 2 in theory? 2 in this experiment? P(2) = P(2) =