Loading...
Loading...
What does "with replacement" mean?
After drawing a card and recording what it is, you put it back in the deck and shuffle thoroughly. The deck returns to its original state before the next draw.
Why does this create independence?
After replacing and shuffling, the deck looks exactly the same as before the first draw. The second draw "doesn't know" what happened on the first draw. Both draws face the same 52-card deck, so they're independent.
The multiplication rule applies:
This is because P(B | A) = P(B) when events are independent.
Draw a card
52 cards in deck
Put it back and shuffle
Deck is restored to original state
Draw again
Still 52 cards - same probabilities!
When you replace the card, the second draw is exactly like the first draw. The deck is always the same, so the outcomes are independent. Without replacement, the first draw changes the deck, creating dependence.