Probability Calculator

Probability is the likelihood of an event occurring, expressed as a number between 0 and 1 (or as a percentage). Odds, on the other hand, represent the ratio of favorable outcomes to unfavorable outcomes.

For example, if the probability of winning is 0.25 (25%), the odds would be 1:3 (1 win for every 3 losses). Probability is generally preferred in statistical analysis, while odds are commonly used in gambling and betting scenarios.

For multiple independent events occurring together (AND), multiply their individual probabilities: P(A and B) = P(A) × P(B).

For either event occurring (OR), use: P(A or B) = P(A) + P(B) - P(A and B).

Remember that events are independent if the outcome of one doesn't affect the other. For dependent events, you need conditional probability formulas.

Combinations (nCr) calculate the number of ways to choose r items from n total items where order doesn't matter. The formula is nCr = n! / (r!(n-r)!).

They're used in lottery calculations (choosing winning numbers), card games (poker hand probabilities), and statistical sampling. For example, choosing 3 numbers from 10 gives us 10C3 = 120 different combinations.

No, probability must always be between 0 and 1 (inclusive). A probability of 0 means the event is impossible, while a probability of 1 means the event is certain to occur.

If your calculation gives a result outside this range, you've made an error and should check your work. Common mistakes include incorrect counting of outcomes or misapplication of formulas.

Probability calculations provide theoretical expectations based on perfect conditions. In real life, results may vary due to factors not accounted for in the model.

However, over large numbers of trials, observed results tend to approach the calculated probabilities. This is known as the Law of Large Numbers, which is why probability is so valuable in fields like insurance, finance, and quality control.