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)

Answer 1

Independent events are those where knowing that one event occurred does not change the probability of the other, i.e. P(A|B) = P(A). Dependent events are those where P(A|B) ≠ P(A), so the occurrence of B changes the likelihood of A; conditional probability is P(A|B) = P(A ∩ B)/P(B). Example of dependent events: drawing two cards without replacement from a standard deck — if the first card was an ace, the probability the second is an ace is 3/51, whereas the unconditional probability of a random card being an ace is 4/52, so the events are dependent.