Advanced Probability
📋 What it is
When cards are NOT replaced, the odds change every draw — this is dependent probability.
🗣️ Coach says
The tricky part: once you draw a card and keep it, the deck is smaller. After drawing one heart, only 12 hearts remain in 51 cards. Real card games are almost all "without replacement", so the odds shift every turn. Update them.
🧠 Memory hook
No put-back = odds SHIFT. After a draw, both the "want" and the "total" drop by the cards gone.
😂 Giggle
Why don't cards ever win arguments?
Because they always fold under pressure!
😲 Whoa!
Card counters in blackjack use exactly this idea — they track which cards are gone to know when the remaining deck favors them.
✅ Quick check: You draw a King and keep it. What is the chance the NEXT card is also a King?
Say your answer out loud first — then reveal.
3/51 — only 3 Kings remain in 51 cards.
Without replacement, both the Kings left (4→3) and total (52→51) drop.
🪄 Trick question: Is the chance of a heart on the 2nd draw the same as the 1st, if you kept the 1st card?
Careful — think it through, then reveal.
No — it depends on what the 1st card was, because the deck changed.
Removing a card without replacing it changes the counts, so the odds change.
🧪 Try it! (2 minutes)
Draw 2 cards without replacing. Before the 2nd draw, say the new odds of a matching suit out loud.