Question

A fair coin is flipped once. The probability of getting a head and a tail simultaneously is. Hence, this is event.

• A. $0$
• B. $1$
• C. $0.5$
• D. an impossible
• E. a certain
• F. an equally possible

Answer 1

Answer: (A), (D)

an impossible

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]