Unit 4

    Cards (137)

    • Binomial distribution
      A probability distribution for a discrete random variable representing the number of successes in N repeated trials
    • Calculating binomial probabilities

      1. List all possible outcomes for X (number of successes)
      2. Calculate probability of each outcome using formula: nCr * p^r * (1-p)^(n-r)
      3. Where n=number of trials, r=number of successes, p=probability of success, (1-p)=probability of failure
    • Binomial distribution

      • Requires success clearly defined and probability of success given
      • Probability of success stays the same from trial to trial
      • Trials are independent
    • Geometric distribution
      Discrete random variable where X is the number of the trial on which the first success occurs
    • Geometric distribution
      • Requires success clearly defined and probability of success given
      • Probability of success stays the same from trial to trial
      • Trials are independent
      • No set number of trials, only care about when first success occurs
    • Mean of binomial distribution
      N * P
    • Standard deviation of binomial distribution
      Square root of N * P * (1-P)
    • Mean of geometric distribution
      1 / P
    • Standard deviation of geometric distribution
      Square root of (1-P) / P
    • Random process
      Generates results that are random or simply unknown and determined by chance
    • Outcome
      The result of a random process
    • Event
      The collection of outcomes
    • Probability
      Quantifying the uncertainty in a random process
    • Long run relative frequency
      The probability of an outcome, found by taking the number of times the outcome occurs divided by the total number of repetitions
    • The law of large numbers states that simulated probabilities tend to get closer to the true probability the more trials we perform
    • The long run relative frequency definition of probability will never be perfect because we can never run infinite simulations or trials
    • Sample space
      A list of all non-overlapping outcomes
    • Probability of an event
      The number of outcomes in favor of the event divided by the total number of outcomes in the sample space
    • The probability of an event is always between 0 and 1 inclusive
    • Complement of an event
      The event does not happen
    • Probability of A and B
      The probability that both events A and B occur at the same time (joint probability)
    • Mutually exclusive events
      Events that cannot happen at the same time
    • Probability of A or B
      The probability that event A only happens, or event B only happens, or both A and B happen (union of events)
    • Conditional probability
      The probability of event A occurring given or on the condition that event B has already or will occur
    • Addition rule
      To find the probability of A or B, take the probability of A plus the probability of B, and subtract the probability of A and B
    • Multiplication rule
      To find the probability of A and B, take the probability of A times the probability of B given that A has already occurred
    • Independent events
      Events where the probability of one event is not affected by the occurrence of the other event
    • If events A and B are independent, the probability of A and B is the probability of A times the probability of B
    • If events A and B are not independent, the probability of A and B is the probability of A times the probability of B given that A has already occurred
    • Two-way table
      A table that shows the relationship between two categorical variables
    • The AP Statistics Exam loves working with two-way tables and probability
    • Probability question with two-way table
      1. Identify the number of outcomes in favor
      2. Identify the total number of outcomes in the sample space
      3. Calculate the probability
    • Joint probability
      The probability of two events occurring together
    • Mutually exclusive
      Two events that cannot occur at the same time
    • Calculating probability with mutually exclusive events
      1. Add the individual probabilities
      2. Subtract the overlap to avoid double counting
    • Conditional probability
      The probability of one event occurring given that another event has occurred
    • Calculating conditional probability
      1. Numerator: Probability of both events
      2. Denominator: Probability of the condition
    • Independence
      Two events are independent if the occurrence of one event does not affect the probability of the other event
    • Checking for independence
      1. Compare the probability of one event to the conditional probability of that event given the other event
      2. If they are equal, the events are independent
    • The probability that Andrea purchases Car 1 is 42% and the probability she purchases Car 2 is 26%
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