Question

What is the largest value of the probability of an event’s occurrence?

Answer 1

Hint: We first explain the concept of empirical probability and how the events are considered. We take the given events and find the number of outcomes. Using the probability theorem of $P\left( A \right)=\dfrac{n\left( A \right)}{n\left( U \right)}$ and the range value $0\le n\left( A \right)\le n\left( U \right)$, we get the possible range of empirical probability of $P\left( A \right)$.

Complete step by step answer:
The largest value for the probability of an event’s occurrence is 1.
Empirical probability uses the number of occurrences of an outcome within a sample set as a basis for determining the probability of that outcome.
We take two events, one with conditions and other one without conditions. The later one is called the universal event which chooses all possible options.
We find the number of outcomes for both events. We take the conditional event A and the universal event as U and numbers will be denoted as $n\left( A \right)$ and $n\left( U \right)$.
We take the empirical probability of the given problem as $P\left( A \right)=\dfrac{n\left( A \right)}{n\left( U \right)}$.
As $0\le n\left( A \right)\le n\left( U \right)$, we get \[\dfrac{0}{n\left( U \right)}\le \dfrac{n\left( A \right)}{n\left( U \right)}\le \dfrac{n\left( U \right)}{n\left( U \right)}\].
Therefore, \[0\le P\left( A \right)\le 1\]. The maximum value can be 1.

Note: We need to understand the concept of universal events. This will be the main event that is implemented before the conditional event. Empirical probabilities, which are estimates, calculated probabilities involving distinct outcomes from a sample space are exact.