# For the experiment of tossing a coin three times, how do you find the probability of getting at least one head?

Apr 26, 2017

$\frac{7}{8.}$

#### Explanation:

The Sample Space $S ,$ associated with the Experiment of

tossing a coin thrice is,

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

$\therefore n \left(S\right) = 8.$

$E =$the Event getting at least one Head

$=$the Event getting no. of Heads 1, or, 2, or 3

$\therefore E = \left\{\begin{matrix}H & H & H \\ H & H & T \\ H & T & H \\ H & T & T \\ T & H & H \\ T & H & T \\ T & T & H\end{matrix}\right\} .$

$\therefore n \left(E\right) = 7.$

$\therefore P \left(E\right) = \frac{n \left(E\right)}{n \left(S\right)} = \frac{7}{8.}$

As an Aliter, we note that,

$E ' =$the Complementary Event of the Event E

$=$the Event getting not a single Head at all

$\therefore E ' = \left\{\left(T , T , T\right)\right\} \Rightarrow P \left(E '\right) = \frac{1}{8.}$

$\therefore P \left(E\right) = 1 - P \left(E '\right) = 1 - \frac{1}{8} = \frac{7}{8.}$

Enjoy Maths.!