A dependent event is one in which the outcome of one event affects the outcome of another. To illustrate this concept, consider the following example:
- Imagine you have a standard deck of playing cards, which contains 52 cards in total.
- If you draw one card from the deck, say the Ace of Hearts, the outcome of your second draw is influenced by your first. Now, there are only 51 cards left in the deck.
- If you want to draw another Ace, your chances have changed because the Ace of Hearts is no longer in the deck. Therefore, the event of drawing a second Ace is dependent on the outcome of the first draw.
In simple terms, the event of drawing a second Ace from this deck is dependent on the first draw because the initial outcome directly affects the total number of cards remaining and the probabilities associated with subsequent draws. This is a classic example of dependent events in probability.