Question

Three different coins are tossed together. Find the probability of getting.
(iii) at least two tails

Answer 1

Solution:

Given: Three coins are tossed simultaneously.

Find total sample space:

Total outcomes $=\left\{HHH,HHT,HTH,THH,HTT,THT,TTH,TTT\right\}$

Total number of possible outcomes $=8$

Find favourable outcomes:

Favourable cases for at least two tails$=\left\{HTT,THT,TTH,TTT\right\}$

Total number of favourable outcomes$=4$

Find probability of getting at least two tails:

$\mathit{P}\mathbf{\left(}\mathit{E}\mathbf{\right)}\mathbf{=}\frac{\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{}\mathit{n}\mathit{o}\mathbf{.}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{f}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{u}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{s}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{no}\mathbf{.}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{p}\mathbf{o}\mathbf{s}\mathbf{s}\mathbf{i}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{es}}$

$$\begin{gathered} \Rightarrow P(gettingatleasttwotails)=\frac{4}{8} \\ \Rightarrow P(gettingatleasttwotails)=\frac{1}{2} \end{gathered}$$

Final Answer: The probability of getting at least two tails is $\frac{\mathbf{1}}{\mathbf{2}}$.