Introduction to probability

Learning Objectives Define fundamental probability terms including experiment, sample space, event, and outcome. Calculate the theoretical probability of a simple event. Understand and apply the rule that the probability of any event is a value between 0 and 1, inclusive. Calculate the probability of the complement of an event. Apply the addition rule to find the probability of two events, distinguishing between mutually exclusive and non-mutually exclusive cases. Differentiate between theoretical and experimental probability. Construct a sample space for a compound experiment, such as rolling two dice or flipping three coins. What are the chances of winning the lottery versus being struck by lightning? 🎲 Probability is the mathematics that helps us answer questions about...

TermDefinitionExample ExperimentAny procedure or action that can be repeated and has a well-defined set of possible results.Flipping a coin, rolling a standard six-sided die, or drawing a card from a deck. Sample Space (S)The set of all possible outcomes of an experiment.For rolling a single die, the sample space is S = {1, 2, 3, 4, 5, 6}. Event (E)A specific outcome or a subset of outcomes from the sample space.When rolling a die, the event 'rolling an even number' corresponds to the subset E = {2, 4, 6}. Theoretical ProbabilityThe probability of an event based on mathematical reasoning and calculation, assuming all outcomes are equally likely.The theoretical probability of rolling a 3 on a fair die is 1/6, as there is one favorable outcome out of six possible outcomes. Experim...

The Basic Probability Formula P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{n(E)}{n(S)} Use this formula to calculate the theoretical probability of an event E, where all outcomes in the sample space S are equally likely. The Range of Probability 0 \le P(E) \le 1 The probability of any event E is always a number between 0 and 1, inclusive. A probability of 0 means the event is impossible, and a probability of 1 means the event is certain. The Complement Rule P(E') = 1 - P(E) The probability that an event will not occur is 1 minus the probability that it will occur. This is often easier than calculating the probability of the complement directly. The General Addition Rule P(A \cup B) = P(A) + P(B) - P(A \cap B)...