Question

What is the probability that a head is obtained, followed by a tail, if a coin is flipped twice?

• A. $1$
• B. $\frac{1}{2}$
  
• C. $\frac{1}{4}$
  
• D. $\frac{3}{4}$
  

Answer 1

The correct option is C $\frac{1}{4}$


Let $\text{P(H)}$ be the probability of obtaining head when a coin is flipped.
Total possible outcomes $=\{H,T\}$
Favorable outcome $=\left\{H\right\}$

Number of favorable outcome $=1$
Total number of outcomes $=2$

$\text{P(H)}=\frac{\text{Number of favorable outcome}}{\text{Total number of outcomes}}$

$\text{P(H)}=\frac{1}{2}$


Let $\text{P(T)}$ be the probability of obtaining tail when a coin is flipped.
Total possible outcomes $=\{H,T\}$
Favorable outcome $=\left\{T\right\}$

Number of favorable outcome $=1$
Total number of outcomes $=2$

$\text{P(T)}=\frac{\text{Number of favorable outcome}}{\text{Total number of outcomes}}$

$\text{P(T)}=\frac{1}{2}$


Let $\text{P(H and T)}$ denotes the probability of obtaining head followed by a tail. This probability would be obtained by multiplying $\text{P(H)}$ and $\text{P(T)}$ as both these events are $\text{Independent events}$.

$\text{P(H and T)}=\text{P(H)}\times \text{P(T)}$

$\text{P(H and T)}=\frac{1}{2}\times \frac{1}{2}$

$\text{P(H and T)}=\frac{1}{4}$


The probabilty $\text{P(H and T)}$ of obtaining a head followed by a tail is $\frac{1}{4}$.

$\underset{–}{AlternateSolution:}$

The sample space $\text{S}$ obtained when a coin is flipped twice is:
$\text{S}=\{HH,HT,TH,TT\}$

We need to find the probabilty $\text{P(H and T)}$ of obtaining a head followed by a tail.
Favorable outcome $=\left\{HT\right\}$

Number of favorable outcome $=1$
Total number of possible outcomes $=4$

$\text{P(H and T)}=\frac{1}{4}$


The probabilty $\text{P(H and T)}$ of obtaining a head followed by a tail is $\frac{1}{4}$.

Therefore, option (c.) is the correct answer.