Find conditional probabilities

Learning Objectives Define conditional probability in their own words. Identify the 'given' event and the event of interest from a word problem. Calculate conditional probability using the formula P(A|B) = P(A ∩ B) / P(B). Determine conditional probabilities from data presented in two-way frequency tables. Use tree diagrams to model and solve conditional probability problems. Differentiate between P(A|B) and P(B|A) and understand why they are not always equal. Apply the concept of conditional probability to solve real-world scenarios. What's the probability that a randomly selected person speaks Spanish, *given* that they live in Mexico? 🇲🇽 This 'given' condition changes everything! This tutorial introduces conditional probability, which is the li...

TermDefinitionExample Conditional ProbabilityThe probability of an event (A) occurring, given that another event (B) has already occurred. It is denoted as P(A|B) and read as 'the probability of A given B'.The probability of drawing a King from a deck of cards, *given* that the card drawn is a face card. Sample SpaceThe set of all possible outcomes of a random experiment.When rolling a standard six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. EventA subset of the sample space; a specific outcome or a set of outcomes.When rolling a die, the event 'rolling an even number' is the set {2, 4, 6}. Intersection of Events (A ∩ B)The event that both event A and event B occur simultaneously. It represents the outcomes that are common to both events.If A is 'rolling an...

The Conditional Probability Formula P(A|B) = \frac{P(A \cap B)}{P(B)} Use this formula to find the probability of event A happening, given that event B has already happened. You must know the probability of B and the probability of both A and B happening. Note that P(B) cannot be zero. The Multiplication Rule for Dependent Events P(A \cap B) = P(B) \times P(A|B) This is a rearrangement of the conditional probability formula. It is used to find the probability of two dependent events both occurring. You multiply the probability of the first event by the conditional probability of the second event.