The probability of an impossible event is 0.
To understand why, let’s first define what we mean by an impossible event. An impossible event is an outcome that cannot occur under any circumstances. For example, if we consider the probability of rolling a 7 on a standard six-sided die, that is an impossible event because the die only has sides numbered 1 through 6.
In probability theory, probabilities are expressed as numbers between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to happen. Since impossible events cannot happen at all, we assign them a probability of 0.
This concept is fundamental to understanding probability, as it helps us differentiate between events that can and cannot occur. So, in summary, when we talk about the probability of something that is entirely impossible, the answer is unequivocally 0.