PROBABILITYTHE 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, 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 unlikely1. It will rain tomorrow:

2. You will win X-factor:

3. You will get above 40% on your probability SAC:

4. 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 PROBABILITYThe experimental probability of an event is based on past experience:

WORKED EXAMPLE: A discus thrower has won 7 of her last 10 competitions.

(a)What is the probability that she will win the next competition?

Pr(win next competition) =

Pr(win next competition) =

(b) What is the probability that she will not win the next competition?

Pr(not winning) =

Pr(not winning) =

The event ‘she will win the next competition’ and

the event ‘she will not win the

next competition’ are

called complementar

y 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

Dice Roll

• What is the probability of rolling a four?

• Number of favourable outcomes = 1 (there is one four on a die)

• Number of possible outcomes = 6 (there are six number on a die)

• Pr(roll a 4) =

• What is the probability of not rolling a four?

• Number of favourable outcomes = 5 (there are five numbers other than a four)

• Number of possible outcomes = 6

• Pr(roll a 4) =

• What do you notice about the probabilities?

• They are complementary; that is, they add up to 1

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 EXAMPLEA 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

• Find the probability that a student likes only Maths

Pr(M) =

• Find the probability that a student likes English

Pr(E or B) = =

• Find the probability that a student likes English or Maths but not both

Pr(not B) = =

MATHS ENGLISH

M M M M M M M

B B B B B B

E E E E E E

QUESTIONS TO DO

• Ex 12A p392 – 1 and 2 (as a class), 3, 4, 7, 8, 9, 12, 13, 15, 16