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

Oct 27, 2015

$\frac{1}{8}$

#### 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:

$\Omega = \left\{\begin{matrix}H & H & H \\ H & H & T \\ H & T & H \\ H & T & T \\ T & H & H \\ T & H & T \\ T & T & H \\ T & T & T\end{matrix}\right\}$

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 $\left(T , T , T\right)$ so we can write that:

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

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

$P \left(A\right) = | A \frac{|}{|} \Omega | = \frac{1}{8}$

So finally we can write the answer:

Probability of getting 3 tails in 3 coin flips is $\frac{1}{8}$.