PROBABILITY THE CHANCE OR LIKELIHOOD OF SOMETHING HAPPENING

CALCULATING PROBABILITY • The chance (probability) of something happening is measured from zero (0) to one (1) • • Pr of 0 means there is absolutely no possible chance of it happening Pr of 1 means that it will definitely happen every time Pr of 0. 5 means there is a 50/50 chance, that is, it will happen half the time The probability of an event can also be described by words and phrases such as impossible, highly unlikely, very unlikely, less than even chance, better than even chance, very likely, highly likely, certain and so on.

KEY DEFINITIONS • Trial: the number of times a probability experiment is conducted. • Outcome: the result of an experiment. For example, if a die is rolled, the outcome is a number between 1 and 6 inclusive. • Event: a desired or favourable outcome. • Equally-likely outcomes: outcomes that have the same chance of occurring. For example, if a coin is tossed, then the chance of tossing a Head is equal to the chance of tossing a Tail. Hence, they are equally-likely outcomes. • Sample space (S): the set of all possible outcomes for an experiment. For example, in rolling a die, the sample space, S, is S = {1, 2, 3, 4, 5, 6}. • Frequency: the number of times an outcome occurs.

QUICK REVIEW Assign a Pr value (between zero and one) and a descriptor (e. g. very likely, impossible…) to the following scenarios: Pr(Richmond winning 2014 GF) = 0. 01, extremely unlikely 1. 2. 3. 4. It will rain tomorrow: You will win X-factor: You will get above 40% on your probability SAC: You will be at school tomorrow:

SAMPLE SPACE • Sample space (S): the set of all possible outcomes for an experiment. • For example, in rolling a die, the sample space is S = {1, 2, 3, 4, 5, 6}. • Write the sample spaces for: • A coin is tossed: S = { • A year level at Lakeview Senior College is chosen at random: S = { • Yr 10 form group form this year is selected randomly: S = {

EXPERIMENTAL PROBABILITY • The event ‘she will win the next competition’ and the event ‘she will not win the next competition’ are called complementary events.

RELATIVE FREQUENCY • The relative frequency of a score is the same as the experimental probability of that score • Use this formula when you are looking at results that are in a table form, and substitute in the known values

THEORETICAL PROBABILITY • The theoretical probability of an event, Pr(E), depends on the number of favourable outcomes and the total number of possible outcomes (that is, the sample space). • It is based on theory rather than past experience (experimental probability)

THEORETICAL PROBABILITY EXAMPLE •

COMPLEMENTARY EVENTS • If we call the outcome we want A, then the opposite of this is written as A' • This is known as the complement of A Pr(A) + Pr(A') = 1

JELLY BEANS • Get into five groups • Write down: • • • How many jellybeans are there? What colours are there? How many of each colour are there? • Do the following questions: write out all your steps properly using the formula • What is the probability of (if you were to pick one at random) getting: • • • A red jellybean? Pr(red) = A blue or a green jellybean? Pr(blue or green) = Not an orange jellybean? Pr(not orange) =

VENN DIAGRAMS

VENN DIAGRAM: WORKED EXAMPLE A survey of 19 Year 10 students found that 7 students liked only Maths and 6 liked only English. Six students enjoyed both. • Represent this information in a Venn diagram ENGLISH MATHS MMMMMMM B B B EEEEEE

QUESTIONS TO DO • Ex 12 A p 392 – 1 and 2 (as a class), 3, 4, 7, 8, 9, 12, 13, 15, 16