Loading...
Loading...
The setup:
Draw a card, check if it's an Ace, put it back, shuffle, draw again. We want BOTH draws to be Aces.
Why is this independent?
Because we put the card back and shuffle! On the second draw, the deck still has all 52 cards, including 4 Aces. The first draw didn't "use up" anything.
Contrast with "without replacement":
If we didn't replace, drawing an Ace first would mean only 3 Aces remain in 51 cards. That changes the probability! But with replacement, both draws face the same 4/52 odds.
4 Aces out of 52 cards
First draw: P(Ace)
Second draw: P(Ace)
Same probability because we replaced the card!
Multiply (independent events)
Result:
| Event | P(single) | P(twice) |
|---|---|---|
| Draw Ace | ||
| Draw Heart | ||
| Draw Face Card | ||
| Draw Red Card |