# With a fair dice what is the probability of rolling a 1?

Nov 6, 2015

The probability is $\frac{1}{6}$

#### Explanation:

In general to calculate probability of an event we have to calculate the number of all elementary events, and the number of events which satisfy condition given by the event we are calculating.

If we are talking about a roll of a dice then:

$\Omega = \left\{1 , 2 , 3 , 4 , 5 , 6\right\}$

There are six possible outcomes in this experiment, so $| \Omega | = 6$

The event $A$ is "rolling a 1", so $A = \left\{1\right\}$. There is only one result which satisfies $A$, so $| A | = 1$

Finally to calculate the probability we have to divide the values calculated:

$P \left(A\right) = | A \frac{|}{|} \Omega | = \frac{1}{6}$