In 3-5 sentences, explain the difference between independent and dependent events when calculating conditional probability, and provide an example of dependent events. Write in paragraph form, limiting at 125 words.

Answer 1

Independent events are those where the occurrence of one event does not affect the probability of the other event occurring, meaning P(A | B) = P(A). In contrast, dependent events are events where the occurrence of one event influences the likelihood of the other event, so P(A | B) ≠ P(A). For example, consider a scenario where a card is drawn from a standard deck of 52 cards. If the first card drawn is a King and it is not replaced, the probability of drawing a second King (event B) changes to 3 out of 51 cards remaining, demonstrating that these events are dependent. Here, the outcome of the first draw directly affects the probabilities involved in the second draw.