The probability of an event measures the likelihood of that event happening. It is represented by a number between 0 and 1, inclusive. The reason why the probability is always between 0 and 1 is because of the way probability is defined.
To understand this, it's helpful to think about extremes. If the probability of an event is 0, it means that the event has no chance of happening. In other words, it is impossible for the event to occur. Likewise, if the probability is 1, it means that the event is certain to happen. In this case, the event is guaranteed to occur.
Any number between 0 and 1 represents a level of uncertainty - the event might happen or might not happen. For example, a probability of 0.5 means that there is a 50% chance of the event occurring and a 50% chance of it not occurring.
Mathematically, the probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, it cannot exceed the total number of outcomes or go below zero. It is bounded by these limits to maintain its interpretability as a measure of likelihood.
So, in summary, the probability of an event must be between 0 and 1 because it represents the likelihood of that event occurring, with 0 indicating impossibility and 1 indicating certainty. This range ensures that the concept of probability remains meaningful and consistent.