GUIDE深度 · Deep dive
Coins, Dice and Cards
Coins use the binomial C(n,k)/2^n; two dice have 36 equally likely outcomes; cards are counted by suit/rank. Write the sample space before counting favorable outcomes.
Coins/dice
Coins: 2^n outcomes.
Two dice: 36 outcomes; sum 7 has 6.
Cards
52 cards, 4 suits x 13 ranks.
26 red cards, 12 face cards.
List the sample space or use a known count first; most errors come from an incomplete sample space rather than arithmetic.
FAQ
How to compute at least k heads?
Sum binomial probabilities from k to n.
Why is sum 7 likely?
It has 6 combinations, the most of any sum.