What is the probability of an event that is impossible?

Answer

The probability of an impossible event is 0.

What is an impossible event in probability theory?

An impossible event in probability theory is an event that cannot occur under any circumstances. The event has a probability of 0, meaning there is no chance the event will take place. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. For an impossible event, the number of favorable outcomes is zero.

$P(\text{impossible event})=\frac{0}{\text{total outcomes}}=0$

$\mathrm{<br>}$An impossible event corresponds to the empty set (null set) in the sample space, indicating no outcomes in the event. Probability values always lie between 0 and 1, where 0 represents impossible events and 1 represents certain events. An impossible event is characterized by having no favorable outcomes in the sample space and a probability of zero.

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