🎲 Probability Calculator

Calculate probability for single and multiple events.

What is a Probability Calculator?

The Probability Calculator determines the likelihood of an event occurring. It calculates the ratio of favorable outcomes to the total number of possible outcomes in a sample space.

P(A) = n(A) / n(S)

📝 In-Depth Guide: Mastering Probability Calculator

Probability is the mathematical study of randomness and uncertainty. It is used in everything from weather forecasting and insurance to gambling and quantum physics. Understanding basic probability helps you make better decisions in high-stakes environments.

Theoretical vs. Experimental Probability

Theoretical probability is based on reasoning. For example, a fair six-sided die has 6 equal outcomes, so the probability of rolling a 4 is exactly 1/6. Experimental probability is based on trials—if you roll a die 100 times and get a "4" twenty times, your experimental probability is 20/100.

Independent vs. Dependent Events

Independent Events: The outcome of one doesn't affect the other (like flipping two separate coins).
Dependent Events: The outcome of the first event changes the probability of the second (like drawing a card from a deck and not replacing it).

The Law of Large Numbers

This law states that as the number of trials increases, the experimental probability will get closer and closer to the theoretical probability. This is why casinos always win in the long run, even if they lose individual hands.

Example

📌 Example Calculation

Rolling a specific number on a 6-sided die: Favorable = 1, Total = 6. Probability = 1/6 ≈ 16.67%.

Frequently Asked Questions

No. By definition, an event cannot be more likely than "certain" (100%) or less likely than "impossible" (0%).

Probability is the ratio of success to total possibilities. Odds are the ratio of success to failure (e.g., probability of 25% is 1:3 odds against).

It means the event has a 50% chance of happening—it is just as likely to occur as it is to not occur.