PROBABILITYThe language of probability

0 1½

Impossible

Very unlikely

Unlikely

Even chance

Likely

Almost certain

Certain

The probability of an event is always between 0 and 1, or0 ≤ P(E) ≤ 1

Example 1Rate these events using the previous scalea) Roll a normal dice and get a number less than 10b) Tomorrows temperature will be 42ºCc) A red card will be drawn from a deck of cards.

a) Certain b) Very unlikelyc) Even chance

Outcomes and sample spacesAn 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 2State the size of the sample space for each of the following experiments.a) Rolling a dieb) Picking a card from a standard deck of cardsc) Guessing the sporting house of a student at IHSd) Making a 3-digit number from the numerals 1, 5 and 7

a) 6 b) 52c) 4d) 6

What is in a standard deck of cards?52 cards4 suits, Spades, Clubs, Diamonds, Hearts2 colours, Black (Spades & Clubs) Red (Diamonds & Hearts)13 cards in each suit2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, APicture 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 3A 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 work1One of these balls is chosen at random.What is the

probability of choosing the following.a) a green ball b) a yellow ballc) a red ball d) 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 CD b) an ABBA CDc) A compilation CD d) a CD that is not a complilation

Today’s work