# 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}

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