Chances

Chances are a way of expressing the likelihood that a particular event will occur. In everyday language, the term refers to the possibility of outcomes, often framed as good or bad fortune. In statistics and mathematics, chance corresponds to a numerical probability, the objective or subjective measure of how likely something is to happen.

Probability theory defines probability as a ratio or proportion of favorable outcomes to total outcomes, and it is commonly expressed as a fraction, a percentage, or odds. For a fair six-sided die, the chance of rolling a three is 1 out of 6, about 16.7%. Odds, by contrast, compare favorable to unfavorable outcomes and are 1 to 5 in this example.

Probability can be objective, based on long-run frequencies (frequentist view), or subjective, reflecting personal beliefs (Bayesian view). It may be independent (the outcome of one event does not affect another) or conditional (the probability changes given new information). The expected value combines probabilities with outcome values to summarize a strategy's average result: EV = Σ p_i · value_i.

Chances influence decision making, risk assessment, science, and everyday planning. Misunderstanding of probability can lead to errors such as overestimating rare events or neglecting base rates. Clear definitions of probability, odds, and independence help describe and compare chances across different contexts.