Pre-Calculus Final: Probability and combinatorics

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Front

How do you calculate the probability of a single event occurring?

Back

The probability of a single event A occurring is calculated using the formula: P(A) = \frac{number \ of \ favorable \ outcomes}{total \ number \ of \ outcomes}.

Front

What is a two-way table in probability?

Back

A two-way table is a statistical table that displays the frequency distribution of two categorical variables, allowing for the analysis of the relationship between them.

Front

What is the formula for combinations?

Back

The formula for combinations is: C(n, r) = \frac{n!}{r!(n-r)!}, where n is the total number of items, r is the number of items to choose, and ! denotes factorial.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, selecting A, B, C is different in permutations but the same in combinations.

Front

What is the general multiplication rule in probability?

Back

The general multiplication rule states that the probability of two events A and B occurring together is P(A and B) = P(A) * P(B|A), where P(B|A) is the conditional probability of B given A.

Front

How do you find the probability of either event A or event B occurring?

Back

The probability of either event A or event B occurring is given by: P(A or B) = P(A) + P(B) - P(A and B).

Front

What is a Venn diagram?

Back

A Venn diagram is a visual representation of the relationships between different sets, often used to illustrate the probabilities of events and their intersections.

Front

What is the probability of drawing a specific card from a standard deck?

Back

The probability of drawing a specific card from a standard deck of 52 cards is P(card) = \frac{1}{52}.

Front

How do you calculate the probability of independent events?

Back

For independent events A and B, the probability of both occurring is: P(A and B) = P(A) * P(B).