Conditional and independent events

Task goals

• Decide whether two events are independent or dependent (conditional) from a description of the situation.
• Build and read a without-replacement probability tree, where the second-stage branch probabilities depend on the first-stage outcome.
• Use P(B given A) notation and calculate a conditional probability from a tree, a Venn diagram, or a two-way table.
• Test independence by comparing P(B) with P(B given A): equal means independent, different means dependent.
• Calculate a combined-event probability (either order, at least one) from a without-replacement tree.
• Critique a probability claim that confuses independence with dependence, including the gambler's fallacy and mistaking a survey correlation for proof of dependence.