Question

Which of the following can be the probability of an event?
(a) -0.04
(b) 1.004
(c) $\dfrac{18}{23}$
(d) $\dfrac{8}{7}$

Answer 1

In an experiment, the probability of an event is the likelihood of that event occurring. Probability is a value between (and including) zero and one. If P(E) represents the probability of an event E, then we write $0\le P\left( E \right)\le 1$ . We have to verify each option by checking whether this condition holds or not.

Complete step-by-step answer:
We have to find which one of the given options can be the probability of an event. Let us recollect what a probability of an event means. In an experiment, the probability of an event is the likelihood of that event occurring. We can say that the probability of an event is a set of outcomes of an experiment.
If P(E) represents the probability of an event E, then we can draw the following conclusions.
(i) We can say that $P\left( E \right)=0$ if and only if E is an impossible event.
(ii) $P\left( E \right)=1$ if and only if E is a certain event.
(iii) If we are given with two events "A" and "B", then P(A) > P(B) if and only if event "A" is more likely to occur than event "B".
(iv) The important rule of probability is that probability is a value between (and including) zero and one, that is, $0\le P\left( E \right)\le 1$ .
Now, let us consider each of the options.
In the option (a), we can see that the probability is negative. According to the condition $0\le P\left( E \right)\le 1$ , we can conclude that -0.04 cannot be the probability of an event.
From option (b), we can see that $1.004>1$ and therefore violate the condition. Hence, 1.004 cannot be the probability of an event.
Now, let us verify option (c). Let us divide 18 by 23.
$\Rightarrow \dfrac{18}{23}=0.783$
We can see that 0.783 is between 0 and 1. Therefore, $\dfrac{18}{23}$ can be the probability of an event.
Now, let us consider option (d). We have to divide 8 by 7.
$\Rightarrow \dfrac{8}{7}=1.142$
We know that 1.142 is greater than 1 and thus violates the condition $0\le P\left( E \right)\le 1$ . Therefore, $\dfrac{8}{7}$ cannot be the probability of an event.

So, the correct answer is “Option C”.

Note: Students must note that in the condition $0\le P\left( E \right)\le 1$ , 0 and 1 are included. The probability of an event can be found by dividing the number of favourable outcomes by the total number of outcomes.
$\Rightarrow P\left( E \right)=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$