Question

If you flip a coin three times, what is the probability of getting tails three times?

Answer 1

`1/8`

Explanation:

To calculate the probability you have to name all possible results first. If you mark a result of a single coin flip as `H` for heads or `T` for tails all results of `3` flips can be written as:

`Omega={(H,H,H),(H,H,T),(H,T,H),(H,T,T),(T,H,H),(T,H,T),(T,T,H),(T,T,T)}`

Each triplet contains results on `1`st, `2`nd and `3`rd coin. So you can see that in total there are `8` elementary events in `Omega`.

`|Omega|=8`

Now we have to define event `A` of getting tails three times.

The only elementary event which satisfies this condition is `(T,T,T)` so we can write that:

`A={(T,T,T)}`
`|A|=1`

Now according to the (classic) definition of probability we can write, that:

`P(A)=|A|/|Omega|=1/8`

So finally we can write the answer:

Probability of getting 3 tails in 3 coin flips is `1/8`.