Question

Which of the following cannot be the probability of an event?
A. $1.5$
B. $\dfrac{3}{5}$
C. $25\% $
D. $0.3$

Answer 1

Hint: Here, we are asked to find the option that cannot be the probability of an event. We all know that the probability of any event must lie between zero and one. Thus, we need to identify the option that does not lie between zero and one. That is, the required option must be greater than one. Also, the value of a probability is always positive so the probability of an event cannot be negative. Hence, we shall just pick the option that contains a value greater than one.

Complete step-by-step answer:
It is a well-known fact that the probability of any event will occur between $0$ and $1$, both inclusive.
That is, $0 \leqslant P\left( A \right) \leqslant 1$ for any event $A$
Let us get into our solution.
A. The given number is $1.5$
We can note that the given number $1.5$ is greater than one.
Thus, option A is not applicable.
B. The given option contains $\dfrac{3}{5}$
$\dfrac{3}{5} = 0.6 < 1$
Thus, $\dfrac{3}{5}$lies between zero and one.
Hence, $\dfrac{3}{5}$can be a probability of an event.
C. The given option contains $25\% $
$25\% = \dfrac{{25}}{{100}}$
$ \Rightarrow 25\% = 0.25 < 1$
Thus, $25\% $lies between zero and one.
Hence, $25\% $can be a probability of an event.
D. The given number is $0.3$
Thus, $0.3 < 1$ lies between zero and one.
Hence, $0.3$can be a probability of an event.

So, the correct answer is “Option A”.

Note: The probability of any event cannot be less than zero and greater than one and it lies in the interval $0 \leqslant P\left( A \right) \leqslant 1$ for any event $A$. The probability of a sure event is $1$ where a sure event occurs always whenever an experiment is performed. An example of a sure event is rolling dice to get a score of less than five.