GUIDE深度 · Deep dive
Classical Probability and Urns
Classical probability assumes equally likely outcomes: P = favorable / total. For urns, check replacement: with replacement the total stays; without replacement both total and favorable counts shrink.
Urns
One draw: P(red)=red/total.
Two without replacement: denominator N(N-1).
Combinations avoid order issues.
Reduce
Write the answer in lowest terms.
Divide numerator and denominator by the GCD.
FAQ
When to use combinations?
When only the selection matters, not the order.
Does the second probability change with replacement?
No; total and favorable counts stay the same.