What is the probability of an impossible event?

The probability of an impossible event is 0. In probability theory, an event is considered impossible if it cannot occur under any circumstances. This means that its probability is zero, indicating no chance of occurrence. Impossible events are typically characterized by outcomes that are logically or physically impossible, such as rolling a six-sided die and getting a result of 7 or flipping a fair coin and it landing on both heads and tails simultaneously.

In probability calculations, the probability of an event is defined as the number of favorable outcomes divided by the number of possible outcomes. Since an impossible event has no favorable outcomes, its probability is always zero. This applies to any situation where the event under consideration is not within the realm of possibility.

It's important to note that an impossible event is different from a highly unlikely or rare event. Highly unlikely events may have a very low probability, but they are still possible to occur given enough trials or an infinite number of possibilities. Impossible events, on the other hand, cannot occur no matter how many trials or possibilities are considered.