PROBABILITY The language of probability 01½ Impossible Very unlikely Unlikely Even chance Likely Almost certain Certain The probability of an event is always between 0 and 1, or 0 ≤ P(E) ≤ 1 Example 1 Rate these events using the previous scale a)Roll a normal dice and get a number less than 10 b)Tomorrows temperature will be 42ºC c)A red card will be drawn from a deck of cards. a)Certain b)Very unlikely c)Even chance

Outcomes and sample spaces An outcome is the actual result of an experiment or game. eg the queen of spades is drawn from a deck of cards. A sample space is the set of all possible outcomes for an experiment or game. eg heads or tails for flipping a coin once. An event is a group of one or more outcomes for an experiment or game. eg the event of rolling a prime number on a die, {2, 3, 5} Under normal conditions, we assume each outcome of an experiment or game is equally likely.

Example 2 State the size of the sample space for each of the following experiments. a)Rolling a die b)Picking a card from a standard deck of cards c)Guessing the sporting house of a student at IHS d)Making a 3-digit number from the numerals 1, 5 and 7 a)6 b)52 c)4 d)6 What is in a standard deck of cards? 52 cards 4 suits, Spades, Clubs, Diamonds, Hearts 2 colours, Black (Spades  & Clubs  ) Red (Diamonds  & Hearts ) 13 cards in each suit 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A Picture cards, Jack, Queen & king

the event E is impossible. If P(E) = 1, Theoretical probability If P(E) = 0, the event E is certain to occur.  0 ≤ P(E) ≤ 1

Example 3 A card is drawn from a standard deck of cards. What is the probability it is a: a)King of spades? b)Queen? c)Green 4? c) P(Green 4) = ♠ 0

Today’s work 1One of these balls is chosen at random.What is the probability of choosing the following. a)a green ballb) a yellow ball c) a red balld) a purple ball 2 Robbie’s CD rack contains 20 CDs. If 8 are by the Beatles, 2 by the Beach Boys, 3 by ABBA, and the rest are compilations, find the probability of randomly choosing the following. a)A beatles CDb) an ABBA CD c) A compilation CDd) a CD that is not a complilation

Today’s work