Question

What is the maximum value of the probability of an event?
A.$\dfrac{1}{2}$
B.$\dfrac{3}{8}$
C.$1$
D. None of these

Answer 1

Hint: In this question we have to find the maximum value of the probability of an event, so first of all we have to define random experiment, event and sample space and then find the relation between event and sample space. After that we have to define probability of the event, then applying the definition of probability and the relation between event and sample space then we can find the maximum value of the probability of an event.

Step by step solution:
Random experiment: An experiment is said to be a random experiment if its outcome cannot be predicted. That is, the outcome of a random experiment does not obey any rule.
Sample Space: The set of all possible outcomes of an experiment is called the Sample Space or Probability Space. It is generally denoted by $S$ and its number of elements by $n(S)$.
Event: Every subset of a sample space is an event. It is generally denoted by E.
Probability: If S be the sample space than the probability of an event $E$ is denoted by $P(E)$ and is defined as
$P(E)=\dfrac{n(E)}{n(S)}$
Where $n(E)$ is the number of elements in the event set $E$, $n(S)$ is the number of elements in the sample space and outcomes are equally likely
Now as per definition, $E$ is subset of $S$, so we can write
$n(E)$ is anything between zero to $n(S)$
So, we can write
$0\le n(E)\le n(S)----(a)$
Now dividing the inequality $(a)$ by $n(S)$ we have

& \dfrac{0}{n(S)}\le \dfrac{n(E)}{n(S)}\le \dfrac{n(S)}{n(S)} \\\ & \Rightarrow 0\le p(E)\le 1------(b) \\\ \end{aligned}$$ Hence, we see from inequality $(b)$ that probability of an event lies between 0 to 1, including 0 and 1. So, the maximum value of the probability of an event is 1. Hence, option C is correct. Note: It should be noted that the definition of the above probability is not true in the following case. 1\. If the events are not equally likely, 2\. If the possible outcomes are infinite, 3\. When the probability is not a rational number.