Probability  a way of calculating the likelihood of an event happening

 

The probability that something will happen can often be calculated by counting the ‘chances’:

 

 

 

 

eg. Probability of getting a 6 on a dice

 

             

 

The probability of ‘A’ taking place is written as P(A).  It is calculated by

 

 

eg.        P(6 on a dice)    =  

            P(      )              

Probabilities are given as FRACTIONS or DECIMALS

 

Range of Possible values

 

The probability of an event NOT being possible is 0

 

The probability of an event DEFINITELY happening is 1

eg.        P(throwing a number less than 7 on a normal dice) = 1

 

 

NOTE: Probabilities range from 0 to 1

 

Probability Space Diagrams

 

Used when finding the probability of two things.

 

eg.        Find the probability of getting ‘heads’ on a coin and an EVEN number on a dice

 

	1	2	3	4	5	6
H		X		X		X
T

                                               

List one set of outcomes at the top and the other down the side.  Use an X to mark the outcomes that answer the question

 

Tree Diagrams

 

Tree diagrams illustrate successive outcomes.  Each branch is one option.  Each set of branches is one set of events.  Total outcomes can be listed at the end.

 

eg.        List the outcomes of tossing a coin 3 times

 

FIRST THROW	SECOND THROW	THIRD THROW	TOTAL OUTCOME
H     T	H   T   H   T	H T H T H T H T	HHH HHT HTH HTT THH THT TTH TTT

 

The probabilities of each event can also be included in the tree diagram

 

eg.        Find the probability of throwing a number greater than 4 twice in a row

 

THROW 1	THROW 2
5, 6                    1, 2, 3, 4	5, 6          1, 2, 3, 4   5, 6          1, 2, 3, 4

 

P(5, 6) and P(5, 6)  

 

Remember

 

P(A) AND P(B)  - along branches             

 

P(A) OR P(B)    - different branches