{
 "source": "https://peabody.kids/flashcards/math-probability-terms",
 "id": "math-probability-terms",
 "title": "Probability and Counting",
 "category": "math",
 "subject": "Math",
 "levels": [
  "6-8",
  "9-12"
 ],
 "description": "Probability vocabulary, rules and counting formulas with simple examples.",
 "tags": [
  "probability",
  "counting",
  "combinatorics"
 ],
 "frontLabel": "Term",
 "backLabel": "Meaning",
 "cards": [
  [
   "Probability",
   "A number from 0 to 1 telling how likely an event is"
  ],
  [
   "Impossible event",
   "Probability 0"
  ],
  [
   "Certain event",
   "Probability 1"
  ],
  [
   "Outcome",
   "One possible result of an experiment"
  ],
  [
   "Event",
   "A set of outcomes"
  ],
  [
   "Sample space",
   "The set of all possible outcomes"
  ],
  [
   "Experiment (trial)",
   "An action with an uncertain result, like rolling a die"
  ],
  [
   "Theoretical probability",
   "Favorable outcomes divided by all equally likely outcomes"
  ],
  [
   "Experimental probability",
   "Number of times it happened divided by number of trials"
  ],
  [
   "Complement of an event",
   "All outcomes where the event does not happen; P(not A) = 1 − P(A)"
  ],
  [
   "Independent events",
   "One event does not change the probability of the other"
  ],
  [
   "Dependent events",
   "One event changes the probability of the other"
  ],
  [
   "Mutually exclusive events",
   "Events that cannot happen at the same time"
  ],
  [
   "Multiplication rule (independent)",
   "P(A and B) = P(A) × P(B)"
  ],
  [
   "Addition rule",
   "P(A or B) = P(A) + P(B) − P(A and B)"
  ],
  [
   "Conditional probability",
   "P(A | B) = P(A and B) / P(B)"
  ],
  [
   "Bayes' theorem",
   "P(A | B) = P(B | A) P(A) / P(B)"
  ],
  [
   "Law of large numbers",
   "With many trials, experimental probability gets close to theoretical probability"
  ],
  [
   "Expected value",
   "The long-run average: sum of each value times its probability"
  ],
  [
   "Random variable",
   "A variable whose value comes from a random process"
  ],
  [
   "Probability of heads on a fair coin",
   "1/2"
  ],
  [
   "Probability of a 4 on a fair die",
   "1/6"
  ],
  [
   "Probability of an even number on a die",
   "1/2"
  ],
  [
   "Probability of a heart from a standard deck",
   "13/52 = 1/4"
  ],
  [
   "Probability of an ace from a standard deck",
   "4/52 = 1/13"
  ],
  [
   "Cards in a standard deck",
   "52"
  ],
  [
   "Probability of two heads in two fair flips",
   "1/4"
  ],
  [
   "Probability of a sum of 7 with two dice",
   "6/36 = 1/6"
  ],
  [
   "Number of outcomes when rolling two dice",
   "36"
  ],
  [
   "Number of outcomes in 3 coin flips",
   "8"
  ],
  [
   "Fundamental counting principle",
   "Multiply the number of choices at each step"
  ],
  [
   "Outfits from 3 shirts and 4 pants",
   "12"
  ],
  [
   "Factorial n!",
   "n × (n − 1) × ... × 1"
  ],
  [
   "Permutation",
   "An ordered arrangement"
  ],
  [
   "Permutation formula",
   "P(n, r) = n! / (n − r)!"
  ],
  [
   "Combination",
   "A selection where order does not matter"
  ],
  [
   "Combination formula",
   "C(n, r) = n! / (r!(n − r)!)"
  ],
  [
   "Ways to arrange 5 books on a shelf",
   "5! = 120"
  ],
  [
   "P(5, 2)",
   "20"
  ],
  [
   "C(5, 2)",
   "10"
  ],
  [
   "C(6, 3)",
   "20"
  ],
  [
   "C(10, 2)",
   "45"
  ],
  [
   "C(n, 0) and C(n, n)",
   "Both equal 1"
  ],
  [
   "Pascal's triangle",
   "A triangle where each number is the sum of the two above it; rows give combinations"
  ],
  [
   "Binomial distribution",
   "The distribution of the number of successes in a fixed number of independent yes/no trials"
  ],
  [
   "With replacement",
   "Each item is put back before the next draw"
  ],
  [
   "Without replacement",
   "Items are not put back; later probabilities change"
  ],
  [
   "Tree diagram",
   "A branching picture that lists outcomes of a multi-step event"
  ],
  [
   "Venn diagram",
   "Overlapping circles showing how sets share members"
  ],
  [
   "Odds",
   "Ratio of favorable outcomes to unfavorable outcomes"
  ],
  [
   "Fair game",
   "A game where each player has the same expected value"
  ],
  [
   "Simulation",
   "Using random numbers or objects to imitate a real chance process"
  ]
 ]
}