Unlikely Event — Definition, Formula & Examples
An unlikely event is an outcome or set of outcomes that has a low probability of happening — typically well below 0.5. The closer its probability is to 0, the more unlikely the event is considered.
An event is called unlikely if is close to 0, meaning the event is expected to occur rarely relative to the total number of equally likely outcomes in the sample space.
How It Works
To decide whether an event is unlikely, calculate its probability and compare it to a scale from 0 to 1. A probability near 0 signals an unlikely event, a probability near 0.5 is roughly even, and a probability near 1 signals a likely event. There is no single universal cutoff, but probabilities below about 0.2 are commonly described as unlikely in middle-school contexts. Crucially, unlikely does not mean impossible — an event with can still happen; it just will not happen often.
Worked Example
Problem: A standard number cube (die) is rolled once. Is rolling a 6 an unlikely event?
Find the probability: There are 6 equally likely outcomes. Only one of them is a 6.
Compare to the scale: Since 0.167 is much closer to 0 than to 0.5, the event is unlikely.
Answer: Rolling a 6 on a single die is an unlikely event because its probability is about 0.167, which is close to 0.
Why It Matters
Understanding which events are unlikely helps you make better predictions in games, sports statistics, and weather forecasting. It also lays the groundwork for more advanced probability topics like expected value and risk assessment.
Common Mistakes
Mistake: Treating unlikely as the same as impossible.
Correction: An impossible event has a probability of exactly 0. An unlikely event has a small but nonzero probability, so it can still occur.