In this section we review the use of listings, tables and tree diagrams to calculate the probabilities of two events.
An unbiased coin is tossed twice.
List all the possible outcomes.
H H 
H T 
T H 
T T 
What is the probability of obtaining two heads?
p(2 heads) = 
What is the probability of obtaining a head and a tail in any order?
p(a head and a tail)  =  = 
A red dice and a blue dice, both unbiased, are rolled at the same time. The scores on the two dice are then added together.
Use a table to show all the possible outcomes.
Blue Dice  

1  2  3  4  5  6  
1  2  3  4  5  6  7 
2  3  4  5  6  7  8 
3  4  5  6  7  8  9 
4  5  6  7  8  9  10 
5  6  7  8  9  10  11 
6  7  8  9  10  11  12 
What is the probability of obtaining:
(i)  a score of 5,  

There are 4 ways of scoring 5, so:
 
(ii)  a score which is greater than 3,  
There are 33 ways of obtaining a score greater than 3, so:
 
(iii)  a score which is an even number?  
There are 18 ways of obtaining a score which is an even number, so:

A card is taken at random from a pack of 52 playing cards, and then replaced. A second card is then drawn at random from the pack.
Use a tree diagram to determine the probability that:
p(Diamond) =  =  and p(not Diamond) =  =  . 
both cards are Diamonds,
p(both Diamonds)  = 
at least one card is a Diamond,
p(at least one Diamond)  =  +  +  = 
exactly one card is a Diamond,
p(exactly one Diamond)  =  +  =  = 
neither card is a Diamond.
p(neither card a Diamond)  = 