impossible event

probability theory

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June 29, 2026

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In probability theory, an impossible event is an event that cannot occur. This is distinct from an unlikely event, which has a low probability but is still possible. The concept of impossibility is crucial in understanding the boundaries of what can happen within a given experiment or scenario.123

Probability theory deals with experiments that can be repeated, with a set of all possible outcomes called a sample space. An event is a subset of this sample space. While unlikely events have a low probability, an impossible event has a probability of zero. For instance, rolling a 7 on a standard six-sided die is an impossible event because the sample space only includes numbers 1 through 6. The quality or state of being improbable is known as improbability.456

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probability theory
The principle of additivity
The impossible event—i.e., the event containing no outcomes—is denoted by Ø. The probability of an event A is written P(A). The principle of addition of probabilities is that, if A₁, A₂,…, A_n are events with A_i ∩ A_j = Ø for all pairs i ≠ j
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The impossible event—i.e., the event containing no outcomes—is denoted by Ø. The probability of an event A is written P(A). The principle of addition of probabilities is that, if A₁, A₂,…, A_n are events with A_i ∩ A_j = Ø for all pairs i ≠ j
Read More