Question

What is the probability of getting $3$ heads in $3$ tosses?

Answer 1

Find the probability of getting $3$ heads in $3$ tosses:

The probability of an event is,

$\mathbf{P}\left(E\right)\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{N}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{f}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{u}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{s}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{s}}$

When a coin is tossed $3$ times, the possible outcomes are:

$TTT,TTH,THT,THH,HHH,HHT,HTH,HTT$

The total number of outcomes $=8$

Let $E$ be the event of getting $3$ heads.

$E=\left\{HHH\right\}$

The number of a favorable outcomes $=1$

Then, the probability of getting $3$ heads is,

$P\left(E\right)=\frac{1}{8}$

Hence, the probability of getting $3$ heads in $3$ tosses is $\frac{1}{8}$.