Random events

The events that are influenced by chance are called random events.

To study chance and its properties we use random experiments, for example: to roll a die, to flip a coin,…

Each possible result of the experiment is called outcome and the set of outcomes is the sample space, E . All the subsets of the sample space are called events.

Example 1: If we roll a die
E = {1, 2, 3, 4, 5, 6} the certain event
A = {obtain an even result} = {2, 4, 6} is an event
Φ = { } is the impossible  event
B = {1} is an elementary event or outcome

Example 2: If we flip two coins
E = {(H, H), (H, T), (T, H), (T, T)}
A= {to obtain at least one head} = {not to obtain 2 tails} = {(H, H), (H, T), (T, H)} 

Exercises:

1-  If we roll two dice:

a) What is the sample space?

b) Describe the events: A={at least one 1}, B={Two 6}, C={The addition is 6}

2.- If we flip one coin. Describe the sample space.

Solutions: 1.- a) E={(1,1),(1,2),(1,3),........,(1,6),(2,1),..................(6,6)}; b) A={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(3,1),(4,1),(5,1),(6,1)}

B={(6,6)};C={(1,5),(2,4),(3,3),(4,2),(5,1)}

2.- E={H,T}