Question

In 3–5 sentences, explain the difference between independent and dependent events when calculating conditional probability, and provide an example of dependent events.(4 points) simple

Answer 1

Independent events are those where knowing that one event occurred does not change the probability of the other, so P(A|B) = P(A). Dependent events are those where the occurrence of one event affects the probability of the other, so P(A|B) ≠ P(A). In conditional probability you must account for this change by using P(A|B) = P(A ∩ B)/P(B) when events are dependent. Example: drawing two cards from a deck without replacement — the probability the second card is an ace depends on whether the first card was an ace, so the events are dependent.