Question

A coin is tossed three times. The probability of getting a head once and a tail twice is
1. $\dfrac{1}{8}$
2. $\dfrac{1}{3}$
3. $\dfrac{3}{8}$
4. $\dfrac{1}{2}$

Answer 1

Hint: To solve this question we will use the basic concept of probability. First we will find the number of total possible outcomes then we will find the number of favorable outcomes. Then we will substitute the values in the basic formula of probability which is given as
$P\left( A \right)=\dfrac{n\left( E \right)}{n\left( S \right)}$
Where, A is an event which we wanted
\[n\left( E \right)=\] Number of favorable outcomes and $n\left( S \right)=$ number of total possible outcomes.

Complete step by step answer:
We have been given that a coin is tossed three times.
We have to find the probability of getting a head once and a tail twice.
Now, we know that when we toss a coin there are two possible outcomes i.e. either head or tail.
So when we toss a coin three times the total number of possible outcomes will be
$\Rightarrow n\left( S \right)=8$
The possible combination of head and tail will be
$\Rightarrow \left\{ HHH \right\},\left\{ HHT \right\},\left\{ HTH \right\},\left\{ HTT \right\},\left\{ THH \right\},\left\{ THT \right\},\left\{ TTH \right\},\left\{ TTT \right\}$
Now, the favorable outcomes of getting a head once and a tail twice will be
$\Rightarrow \left\{ HTT \right\},\left\{ THT \right\},\left\{ TTH \right\}$
So the number of favorable outcomes will be
$\Rightarrow n\left( E \right)=3$
Now, the probability of getting a head once and a tail twice will be
$\begin{align}
  & \Rightarrow P\left( A \right)=\dfrac{n\left( E \right)}{n\left( S \right)} \\
 & \Rightarrow P\left( A \right)=\dfrac{3}{8} \\
\end{align}$
Hence we get the probability of getting a head once and a tail twice is $\dfrac{3}{8}$.

So, the correct answer is “Option 3”.

Note: The point to be noted is that when we calculate the probability of occurrence of any event the value should be lie between 0-1. The value of probability cannot exceed one. Probability value higher than one means probability greater than $100%$ and it is not possible.