Question

Which number cannot represent a probability?
(A) $\dfrac{2}{3}$
(B) $1.5$
(C) $15\%$
(D) $0.7$

Answer 1

Hint : In the question, we are given a certain set of numbers and we have to find which number cannot be a probability. For this firstly we should understand that in an experiment, probability is the measure of likelihood of an event to occur. Probability is a value between (and including) zero and one. If $P\left( E \right)$ represents the probability of an event, then we can write $0 \leqslant P\left( E \right) \leqslant 1$ .On the basis of these concepts we will check each option and find whether it can be a probability or not.

Complete step-by-step answer :
We have to find which one of the given options can not be a probability of an event. Let us recollect what a probability of an event means. The probability is the measure of likelihood of an event to occur. The important rule of probability is that probability is a value between (and including) zero and one i.e., if $P\left( E \right)$ represents the probability of an event, then we can write $0 \leqslant P\left( E \right) \leqslant 1$
Now let us consider each of the options.

In the option (a), the first number we are given is $\dfrac{2}{3}$ . Let us divide $2$ by $3$
$\Rightarrow \dfrac{2}{3} = 0.667$
Here we can see that $0.667$is between $0$ and $1$ .
$\therefore \dfrac{2}{3}$ can be the probability of an event.

Now from option (b), the given number is $1.5$
Here we can see that $1.5 > 1$ and therefore violate the condition. Hence, $1.5$ cannot be the probability of an event.

Now, let us verify option (c), the given term is $15\%$
$\Rightarrow 15\% = \dfrac{{15}}{{100}} = 0.15$
Here we can see that $0.15$is between $0$ and $1$ .
$\therefore 15\%$ can be the probability of an event.

Now, let us consider option (d), the given number is $0.7$
Here we can see that $0.7$is between $0$ and $1$ .
$\therefore 0.7$ can be the probability of an event.
Thus, from the above calculation we observe that only $1.5$ can not be the probability of an event.
So, the correct answer is “Option C”.

Note : Students must note that in the given condition $0 \leqslant P\left( E \right) \leqslant 1$ , $0$ and $1$ are included. Probability of an event, $P\left( E \right) = 0$ if and only if $E$ is an impossible event. And probability of an event, $P\left( E \right) = 1$ if and only if $E$ is a certain event. And the sum of probabilities will always be equal to $1$