Probability Calculator
Explore a wide range of probability calculations: coin flips, dice rolls, card draws, combinations, permutations, conditional probability, and custom event scenarios. Visualize distributions and learn practical statistical applications, all on one page optimized for easy PDF export.
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Coin Flip Calculator
Educational Content: Probability Distributions & Applications
About Probability
Probability quantifies uncertainty, expressing how likely an event is to occur. It ranges from 0 (impossible) to 1 (certain), and is used in science, business, and everyday life to inform decision-making.
Common Distributions:
- Binomial: Probability of a given number of successes in a sequence of independent yes/no experiments (e.g. coin flips).
- Normal (Gaussian): Used for naturally variable phenomena: heights, errors, etc.
- Uniform: All outcomes equally likely (e.g. single fair die or card pick).
- Hypergeometric: Probability for draws without replacement (e.g. cards from a deck).
- Poisson: Number of events in a fixed interval (not shown above, but common for rare events).
Practical Uses:
- Games of chance: Gambling, board games, lotteries.
- Quality control: Checking defect rates in products.
- Forecasting: Weather or market predictions.
- Science & research: Medical trials, genetics, reliability engineering.
- Risk assessment: Insurance, project management.
Combinations vs Permutations
- Combination (nCr): Number of ways to choose r objects from n where order does not matter.
- Permutation (nPr): Number of ways to choose r objects from n where order matters.
Conditional Probability
If event B has occurred, the probability that A also occurs: P(A|B) = P(A ∩ B) / P(B). This is fundamental to statistical inference and Bayes' theorem.