# Suppose that you toss a coin and roll a die. What is the probability of obtaining tails and a five?

Oct 29, 2015

The probability is $P \left(A\right) = \frac{1}{12}$

#### Explanation:

First we have to find all possible result of the experiment.
If we denote $H$ for heads and $T$ for tails we can write, that:

Omega={(H,1);(H,2);(H,3);(H,4);(H,5);(H,6);(T,1);(T,2);(T,3);(T,4);(T,5);(T,6)}

So we can see that there are $12$ elements in $\Omega$. We can write, that: $| \Omega | = 12$

If we denote $A$-event of obtaining tails and a five, then we can also write, that:

$A = \left\{\left(T , 5\right)\right\}$, so $| A | = 1$

Now we can calculate the probability using the classic definition.

$P \left(A\right) = | A \frac{|}{|} \Omega | = \frac{1}{12}$