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Introductory Statistics: Probability Concepts and Counting

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Terms in this set (20)

  • What is probability?

    Probability is how often something occurs or is expected to occur.

  • What does probability theory help us do?

    It helps make decisions about populations, often using the Rare Event Rule.

  • What is the Rare Event Rule for Inferential Statistics?

    If the probability of an observed event is extremely small under an assumption, the assumption is probably not correct. Such an event is called statistically significant.

  • What is a tree diagram used for in probability?

    A tree diagram helps find the sample space by showing all possible outcomes of a procedure.

  • What is the Fundamental Counting Principle?

    Multiply the number of possible outcomes for each part of a procedure to find the total possible outcomes.

  • How do you find the sample space for one roll of a six-sided die?

    The sample space is {1, 2, 3, 4, 5, 6}, representing all possible outcomes.

  • How do you find the sample space for two coin flips?

    The sample space is {HH, HT, TH, TT}, representing all possible outcomes.

  • What is a factorial and how is it denoted?

    The factorial, denoted \(!\), is the product of decreasing positive whole numbers, e.g., \(4! = 4 \cdot 3 \cdot 2 \cdot 1 = 24\).

  • What is the value of 0 factorial?

    By definition, \(0! = 1\).

  • How do you calculate the probability of an event A?

    \(P(A) = \frac{\text{number of occurrences of A}}{\text{total number of outcomes}}\)

  • What are the possible values for any probability?

    Probability values are between 0 and 1, inclusive. 0 means impossible, 1 means certain.

  • What is classical probability?

    Classical probability assumes each event has an equal chance of occurring and is calculated without producing results.

  • What is relative frequency probability?

    Relative frequency probability is calculated from recorded data of a procedure and is an approximation.

  • How many outcomes are there when flipping a coin, spinning a spinner with 3 colors, then flipping another coin?

    Use the Fundamental Counting Principle: 2 (coin) × 3 (spinner) × 2 (coin) = 12 possible outcomes.

  • How many outfits can you make with 4 shirts, 3 pairs of pants, and 3 pairs of shoes?

    Multiply: 4 × 3 × 3 = 36 possible outfits.

  • How many passwords can be formed with 5 capital letters if each letter can be used only once?

    Calculate \(5! = 120\) possible passwords.

  • How many ways can you arrange 6 books on a shelf?

    There are \(6! = 720\) ways to arrange the books.

  • What does it mean if an event is statistically significant?

    It means the event is very unlikely to happen by chance, indicating the assumption may be incorrect.

  • What is a simple event?

    A simple event is an event that cannot be broken down into simpler components.

  • What is the sample space?

    The sample space is the set of all possible outcomes of a procedure.