Geometry Test-Chapter 12 Flashcards

Probability Concepts

• Sample Space: The complete set of all possible outcomes in a probability scenario.
• Outcome: A specific result from a probability experiment.
• Probability of an Event: Represents the chances of an event occurring, quantified as a percentage (0% to 100%).
• Decimal, Fraction, Percent Forms: Probability can be expressed in decimal (rounded to 3 decimals), fraction (simplified), or percent (nearest tenth).

Standard Deck of Cards

• A standard deck has 52 cards divided into 4 suits with 13 cards each.
• Contains a total of 12 face cards (3 per suit).

Theoretical vs. Experimental Probability

• Theoretical Probability: Calculated using favorable outcomes divided by total possible outcomes.
• Experimental Probability: Determined by the ratio of successful outcomes to the number of trials conducted.

Independent and Dependent Events

• Independent Events: The occurrence of one event does not influence another; formula: P(A and B) = P(A) x P(B).
• Dependent Events: One event affects another; formula: P(A and B) = P(A) x P(B|A).

Complementary Events

• Probability of the Complement of an Event: A̅ = 1 - P(A), where A̅ is the complement of event A.

Joint and Marginal Frequencies

• Joint Frequency: The value in each cell of a two-way table.
• Marginal Frequency: The sum of rows and columns in a table indicating totals.
• Conditional Relative Frequency: Relationship between joint and row totals (joint relative frequency divided by row total).

Overlapping and Mutually Exclusive Events

• Overlapping Events: Events that may occur simultaneously; P(A) + P(B) - P(A and B) = P(A or B).
• Disjoint Events: Events that cannot happen at the same time; P(A) + P(B) = P(A or B).

Probability Examples

• Examples illustrate real-world applications, such as determining probabilities of drawing specific cards from a deck or calculating conditional probabilities based on consumer behavior.

Combinations and Permutations

• Permutation: Arrangement of objects where order is important. Example: Arranging the letters in "JUNE."
• Combination: Selection of objects where order does not matter. Example: Choosing side dishes or songs.

Factorials and Arrangements

• Factorial: Product of an integer and all positive integers below it; represents total arrangements.
• Examples of arrangements: Calculating how many orders students can finish in races or how many ways songs can be played.

Probability Distribution

• A function providing the probabilities for all possible values of a random variable; total probability must equal 1.

Binomial Distribution

• Formulated for scenarios with two possible outcomes (success or failure), characterized by the number of trials (n) and the probability of success (P).

Specific Example Calculations

• Binomial example: Survey of dentist visits with probabilities calculated for up to 5 selected adults. The most likely outcome indicated that 3 out of 5 adults had visited a dentist in the last year.