Question

The probability of an impossible event is _____?
\[
  A.{\text{ }}3 \\
  B.{\text{ 2}} \\
  C.{\text{ 1}} \\
  D.{\text{ 0}} \\
 \]

Answer 1

Hint: Probability is defined as the ratio of number of favorable outcomes to the total number of outcomes. An impossible event is an event that cannot happen. So, for an impossible event the total number of favorable outcomes is zero.

Complete step-by-step answer:

Since, we know that for an impossible event number of favorable outcomes $ = 0$
Let the total number of outcomes may be anything (say) $n$
So, the probability of an impossible event is
$
   = \dfrac{{{\text{number of favorable events}}}}{{{\text{total number of events}}}} \\
   = \dfrac{0}{{\text{n}}} \\
   = 0 \\
 $
Therefore the probability of an impossible event is zero.
So, option D is the correct option.

Note: Probability exists on a scale from $0{\text{ to 1}}$ , with $0$ being defined as an impossible event and being $1$ defined as a sure event. Everything between $0{\text{ and 1}}$ is possible and with increasing probability, events become more likely.