NSML Assumed Knowledge

Last updated: 2021-11-28

These facts will be assumed without any further commentary on contests and problems.

• All random selection is fair unless stated otherwise. (See below for details.)
• Cards
  • A standard deck of 52 cards has 13 ranks and 4 suits each.
  • Ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.
  • Suits: clubs, hearts, diamonds, spades.
  • Note: the two jokers found in some decks of cards will never be considered.
  • Vocabulary: draw or deal from a deck.
• Dice
  • A standard n-sided die has possible outcomes {1,2, …, n}.
  • Vocabulary: die (singular) and dice (plural) are rolled.
  • A fair die is one in which all outcomes are equally likely.
• Coins
  • A standard coin has two outcomes: Heads and Tails.
  • Vocabulary: a coin is flipped or tossed.
  • A fair coin is one in which the probability of each outcome is 1/2.
• Letters
  • There are 26 letters in the standard alphabet.
  • Vocabulary
    • Vowels are A, E, I, O, and U.
    • Consonants are all 21 other letters, including Y.
    • Word means any string of letters.
• Fairness
  • Every possible outcome is equally likely.
  • Unless a problem explicitly explains selection is unfair, fair choice should be assumed.