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# 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.

The most common events are:

–The impossible event, ф, which has no chance of occurring: ф ={ }

–The sure event, E, which contains the whole sample space.

Compound event which contains more than one outcome.

Example: 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

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}