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Probability Calculator
Fraction: 1/6
Odds: 1:5
Understanding Probability (Without the Headache)
Probability is just a fancy way of saying "how likely is this to happen?" It's the math of uncertainty. Whether you're flipping a coin, rolling dice, or checking the weather forecast, you're using probability.
Probability vs. Odds
This is where most people get tripped up. They sound the same, but they aren't.
- Probability: Successes / Total Attempts (e.g., 1/6 for rolling a 6).
- Odds: Successes : Failures (e.g., 1:5 for rolling a 6).
💡 Expert Insight from Dr. Alex M., Ph.D.
"The most counter-intuitive thing about probability? Independence. If you flip a coin and get Heads 10 times in a row, the chance of the next flip being Heads is still exactly 50%. The coin has no memory. Don't fall for the 'Gambler's Fallacy' thinking a Tails is 'due'."
⚠️ Common Mistake: Adding Probabilities Wrong
If you want the probability of Event A
OR Event B happening, you add them (if they are mutually exclusive).
If you want Event A AND Event B happening, you multiply them (if they are
independent).
Don't mix these up! Adding when you should multiply leads to probabilities >
100%, which is impossible.
Reviewed by Dr. Alex M., Ph.D.
Mathematics Professor
Last updated: November 2025
Frequently Asked Questions
What is the difference between Probability and Odds?
Probability compares what you want to happen vs. EVERYTHING that could happen (1 in 6 chance of rolling a die). Odds compare what you want to happen vs. what you DON'T want to happen (1:5 odds of rolling a 6). It's subtle but important for gambling and statistics.
How do I calculate probability?
Simple formula: Favorable Outcomes / Total Possible Outcomes. If there are 5 red marbles and 15 blue ones (20 total), the probability of picking red is 5/20, which simplifies to 1/4 or 25%.
Can probability be greater than 1?
Nope. Probability is always between 0 (impossible) and 1 (certain). If you get 1.5, you did the math wrong. Percentages can't go over 100% in probability.
What does 'independent events' mean?
It means one event doesn't affect the other. Flipping a coin twice? The first flip doesn't change the second flip. It's still 50/50. This is where gamblers get it wrong (The Gambler's Fallacy).
How do I convert odds to probability?
If odds are A:B, probability is A / (A+B). Example: Odds of 1:4 means probability is 1 / (1+4) = 1/5 or 20%.