Question

A fair coin is flipped once. What is the probability of getting a head and a tail simultaneously? Write the event type.

• A. $0$, Certain event
• B. $1$, Impossible event
• C. $0$, Impossible event
• D. $1$, Certain event

Answer 1

The correct option is C $0$, Impossible event

For flipping a fair coin,
$\text{Sample Space}$ $=\left\{\text{H, T}\right\}$
$\therefore$ Total number of outcomes $=2$

For getting a head and a tail simultaneously,
$\text{Favorable outcomes}$ $=\left\{\text{HT, TH}\right\}$, which do not belong to the sample space.
$\therefore$ Number of favorable outcomes $=0$
[Favorable outcomes must be taken from sample space only]

Hence, the probability of getting a head and a tail simultaneously,

$\text{P(getting a head and a tail simultaneously)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{0}{2}=0$

$\therefore$ Probability of getting both, a head and a tail is $0$. That implies the event is impossible.
[Events with zero probability are called impossible events]

Hence, option (c.) is the correct choice.