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

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Answer 1 · 2015-10-29T20:37:30

The probability is $P(A)=1/12$

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:

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

Now we can calculate the probability using the classic definition.

$P(A)=|A|/|Omega|=1/12$