Question

Match the following for flipping a fair coin. (P, H and T stand for probability, head and tail, respectively)

• A. $0$
• B. $\frac{1}{2}$
• C. $1$

Answer 1

Suppose, a fair coin is flipped once.
Possible outcomes= $\text{{H, T}}$
$\therefore$ Number of possible outcomes= 2

Now, for finding out the probability of head,
favorable outcome= $\text{{H}}$
$\therefore$ Number of favorable outcome= 1

Hence, $\text{P (H)}=\frac{\text{Number of favorable outcome}}{\text{Total number of outcomes}}$
$\Rightarrow \underset{–}{\text{P ( H)}=\frac{1}{2}}$

Similarly, for finding out the probability of tail,
favorable outcome= $\text{{T}}$
$\therefore$ Number of favorable outcome= 1

Hence,
$\text{P (T)}=\frac{\text{Number of favorable outcome}}{\text{Total number of outcomes}}$
$\Rightarrow \text{P ( T)}=\frac{1}{2}$

Thus, $\underset{–}{\text{P (H) + P (T)}=\frac{1}{2}+\frac{1}{2}=1}$


Lastly, we need to find out $\text{P (neither H nor T)}$.

As we know, flipping a coin always results in either head $\text{(H)}$ or tail $\text{(T)}$. Thus, the outcome neither head $\text{(H)}$ nor tail $\text{(T)}$ is impossible.

$\therefore$ $\underset{–}{\text{P (neither H nor T)}=0}$


$\underset{–}{\text{Remark}}$
If the fair coin is flipped as many times, all the probabilities discussed above will remain the same.