Question

In a simultaneous throw of three coins, what is the probability of getting at least $2$ tails.

• A. $\frac{1}{8}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

The correct option is C

$\frac{1}{2}$

Explanation for the correct option.

Find the probability.

When three coins are tossed simultaneously the sample space $S$ is given as:

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

So the total number of outcomes is $n\left(S\right)=8$.

Let $A$ be the event that tails occur at least twice, then

$A=\left\{HTT,THT,TTH,TTH\right\}$

So the number of favorable outcomes is $n\left(A\right)=4$.

So the probability of getting at least $2$ tails is given as:

$\begin{array}{rcl}P\left(A\right)& =& \frac{n\left(A\right)}{n\left(S\right)}\\ & =& \frac{4}{8}\\ & =& \frac{1}{2}\end{array}$

Hence, the correct option is C.