Unit 6 Discrete Probability

What is a discrete distribution??A probability distribution where only whole number outcomes are possible (e.g., dice rolls, coin flips);
What are the 4 conditions for a binomial distribution??1. Fixed number of trials 2. Only two outcomes (success/failure) 3. Constant probability 4. Independent trials;
What is the binomial distribution used for??Finding the probability of getting a certain number of successes in repeated trials;
What does "success" mean in a binomial distribution??Any outcome you're measuring (e.g., winning, catching a shiny Pokémon, getting sick) – it doesn’t always mean something positive;
What is an example of a binomial distribution??Flipping a coin 50 times and calculating the chance of getting exactly 20 heads;
What is the expected value (mean) of a binomial distribution??Multiply the number of trials (n) by the probability of success (π): μ = n × π;
What is a Poisson distribution??A probability model used for counting events in a fixed interval of time or space when events happen at a steady average rate;
When do you use a Poisson distribution??When events happen randomly but at a known average rate, and each event is independent;
What is an example of a Poisson distribution??Catching fish during a 3-hour boat trip where you usually catch 8 fish on average;
What is the expected value (mean) of a Poisson distribution??The mean is the average rate (λ or μ), which also equals the variance in a Poisson distribution;
What does "discrete variable" mean??A variable with specific, countable values (like 0, 1, 2…);
What does "continuous variable" mean??A variable that can take any value within a range, including decimals (e.g., time, weight, temperature);
What are the 2 rules for any probability distribution??1. Each probability must be between 0 and 1 2. All probabilities must add up to 1 (100%);
How do you find expected value for a discrete variable??Multiply each outcome by its probability, then add all the results together;
Why is wording important in binomial problems??Phrases like “fewer than,” “or more,” and “exactly” affect which values you include when calculating probability;