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Probability and Counting

Probability vocabulary, rules and counting formulas with simple examples.

52 cardsGrades 6–8, Grades 9–12#probability#counting#combinatorics

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  • ProbabilityTerm
    A number from 0 to 1 telling how likely an event is
  • Impossible eventTerm
    Probability 0
  • Certain eventTerm
    Probability 1
  • OutcomeTerm
    One possible result of an experiment
  • EventTerm
    A set of outcomes
  • Sample spaceTerm
    The set of all possible outcomes
  • Experiment (trial)Term
    An action with an uncertain result, like rolling a die
  • Theoretical probabilityTerm
    Favorable outcomes divided by all equally likely outcomes
  • Experimental probabilityTerm
    Number of times it happened divided by number of trials
  • Complement of an eventTerm
    All outcomes where the event does not happen; P(not A) = 1 − P(A)
  • Independent eventsTerm
    One event does not change the probability of the other
  • Dependent eventsTerm
    One event changes the probability of the other
  • Mutually exclusive eventsTerm
    Events that cannot happen at the same time
  • Multiplication rule (independent)Term
    P(A and B) = P(A) × P(B)
  • Addition ruleTerm
    P(A or B) = P(A) + P(B) − P(A and B)
  • Conditional probabilityTerm
    P(A | B) = P(A and B) / P(B)
  • Bayes' theoremTerm
    P(A | B) = P(B | A) P(A) / P(B)
  • Law of large numbersTerm
    With many trials, experimental probability gets close to theoretical probability
  • Expected valueTerm
    The long-run average: sum of each value times its probability
  • Random variableTerm
    A variable whose value comes from a random process
  • Probability of heads on a fair coinTerm
    1/2
  • Probability of a 4 on a fair dieTerm
    1/6
  • Probability of an even number on a dieTerm
    1/2
  • Probability of a heart from a standard deckTerm
    13/52 = 1/4
  • Probability of an ace from a standard deckTerm
    4/52 = 1/13
  • Cards in a standard deckTerm
    52
  • Probability of two heads in two fair flipsTerm
    1/4
  • Probability of a sum of 7 with two diceTerm
    6/36 = 1/6
  • Number of outcomes when rolling two diceTerm
    36
  • Number of outcomes in 3 coin flipsTerm
    8
  • Fundamental counting principleTerm
    Multiply the number of choices at each step
  • Outfits from 3 shirts and 4 pantsTerm
    12
  • Factorial n!Term
    n × (n − 1) × ... × 1
  • PermutationTerm
    An ordered arrangement
  • Permutation formulaTerm
    P(n, r) = n! / (n − r)!
  • CombinationTerm
    A selection where order does not matter
  • Combination formulaTerm
    C(n, r) = n! / (r!(n − r)!)
  • Ways to arrange 5 books on a shelfTerm
    5! = 120
  • P(5, 2)Term
    20
  • C(5, 2)Term
    10
  • C(6, 3)Term
    20
  • C(10, 2)Term
    45
  • C(n, 0) and C(n, n)Term
    Both equal 1
  • Pascal's triangleTerm
    A triangle where each number is the sum of the two above it; rows give combinations
  • Binomial distributionTerm
    The distribution of the number of successes in a fixed number of independent yes/no trials
  • With replacementTerm
    Each item is put back before the next draw
  • Without replacementTerm
    Items are not put back; later probabilities change
  • Tree diagramTerm
    A branching picture that lists outcomes of a multi-step event
  • Venn diagramTerm
    Overlapping circles showing how sets share members
  • OddsTerm
    Ratio of favorable outcomes to unfavorable outcomes
  • Fair gameTerm
    A game where each player has the same expected value
  • SimulationTerm
    Using random numbers or objects to imitate a real chance process

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