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 \[1\]