Theoretical and experimental probability

Learning Objectives Define theoretical and experimental probability. Calculate the theoretical probability of simple and compound events. Determine the experimental probability of an event from given data. Compare and contrast theoretical and experimental probabilities for a given scenario. Explain how the number of trials affects the relationship between experimental and theoretical probability. Use probability to make and critique predictions about real-world situations. If you flip a fair coin 10 times, are you guaranteed to get exactly 5 heads and 5 tails? 🤔 Let's explore the difference between what *should* happen and what *actually* happens! This tutorial will guide you through two fundamental types of probability: theoretical and experimental. You will learn ho...

TermDefinitionExample ExperimentA repeatable procedure with a set of well-defined possible results.Rolling a six-sided die, flipping a coin, or spinning a spinner. Sample Space (S)The set of all possible outcomes of an experiment.For rolling a standard six-sided die, the sample space is S = {1, 2, 3, 4, 5, 6}. Event (E)A specific outcome or a set of outcomes from an experiment; a subset of the sample space.When rolling a die, the event of 'getting an even number' is the set E = {2, 4, 6}. Theoretical ProbabilityThe probability of an event based on mathematical reasoning and calculation, assuming ideal conditions. It's what we expect to happen.The theoretical probability of rolling a 3 on a fair six-sided die is 1/6, because there is one favorable outcome (rolling a 3) out o...

Theoretical Probability Formula P(E) = \frac{n(E)}{n(S)} Use this when all outcomes in the sample space are equally likely. P(E) is the probability of event E, n(E) is the number of favorable outcomes for event E, and n(S) is the total number of outcomes in the sample space. Experimental Probability Formula P(E) = \frac{\text{Number of times event E occurred}}{\text{Total number of trials}} Use this formula to calculate the probability based on data collected from an actual experiment. It is also known as relative frequency. The Law of Large Numbers As the number of trials increases, the experimental probability of an event will tend to approach its theoretical probability. This is a conceptual rule, not a calculation formula. It explains why experimental results fro...