Binomial
Use for repeated independent trials with the same p
Coin flips are binomial because each flip has the same probability of heads and one flip does not change the next one.
Hypergeometric
Use for draws without replacement from a fixed population
Card hands are hypergeometric because each drawn card changes what remains in the deck.
Quick test
Ask what happens after one success
- If the next trial still has the same success probability, think binomial.
- If the population has changed and the next draw has a different success probability, think hypergeometric.