Question

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

Answer 1

The probability is `P(A)=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={(T,5)}`, so `|A|=1`

Now we can calculate the probability using the classic definition.

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