Each individual element of the sample space, a single possible result of a chance experiment, is called an outcome.
Missing Word
outcome
An outcome is one result of an experiment, such as rolling a 4. The sample space is the set of all outcomes, and an event is any collection of them.
Category: Basic Terminology
Question 2
The complement of event A, written A', consists of all results in the sample space that are not in A.
Missing Word
complement
The complement of A holds every result outside A, so A and its complement together make up the whole sample space. That is why the probability of A' equals 1 minus the probability of A.
Category: Basic Terminology
Question 3
Two events are independent when knowing that one occurred does not change the probability of the other.
Missing Word
independent
Independent events do not affect each other's chances, so the probability of both occurring is the product of their separate probabilities. Separate coin flips are a standard example.
Category: Independence and Exclusivity
Question 4
To get the chance of heads on both of two fair coin flips, multiply 0.5 by 0.5 to get 0.25.
Missing Word
multiply
Separate coin flips do not affect each other, so the probability that both events happen is the product of their probabilities. This multiplication rule for independent events gives (0.5)(0.5) = 0.25.
Category: Multiplication Rule
Question 5
The intersection of events A and B, written A AND B, contains only the results that belong to both events.
Missing Word
intersection
The intersection is the overlap of two events. In a Venn diagram it is the region shared by both circles, and for mutually exclusive events it is empty.
Category: Basic Terminology
Question 6
Written A OR B, the event made up of every result in A or in B is called the union of A and B.
Missing Word
union
The union combines every result in either event, counting results in both just once. Its probability comes from the addition rule.
Category: Basic Terminology
Question 7
A Venn diagram shows events as circles drawn inside a rectangle that stands for the sample space.
Missing Word
Venn
A Venn diagram makes overlaps between events visible: the shared region of two circles is A AND B, and circles that do not touch show mutually exclusive events.
Category: Tree and Venn Diagrams
Question 8
In a two-way table, each box where one row meets one column holds a single count and is called a cell.
Missing Word
cell
A cell of a two-way (contingency) table counts the observations that fall in both its row category and its column category. Dividing a cell count by the grand total gives a joint probability.
Category: Contingency Tables
Question 9
Dealing cards from a deck one at a time without putting any back makes the successive draws dependent, since each card dealt changes what remains.
Missing Word
dependent
Events are dependent when one changes the probability of the other. Without replacement, the makeup of the deck shifts after every card, so later draws depend on earlier ones.
Category: Independence and Exclusivity
Question 10
In probability the word OR is inclusive, so A OR B also contains the results that belong to both events.
Missing Word
inclusive
Inclusive OR means the outcomes in both events count as part of A OR B. That is why the addition rule subtracts P(A AND B) once, so those shared outcomes are not counted twice.
Category: Addition Rule
Question 11
Rolling two fair six-sided dice, a red one and a green one, gives a sample space of 36 equally likely ordered pairs.
Missing Word
36
The red die can show any of 6 faces and the green die any of 6 faces, and each face of one can pair with each face of the other, so there are 6 x 6 = 36 ordered pairs. Order matters because a red 2 with a green 5 is a different result from a red 5 with a green 2.
Category: Basic Terminology
Question 12
In a tree diagram, each line segment that shows one possible result at a stage, labeled with its probability, is called a branch.
Missing Word
branch
Branches split from each point of a tree diagram, one for each possible result at that stage. Probabilities are multiplied along a path of branches.
Category: Tree and Venn Diagrams
Question 13
Each single repetition of a chance experiment, such as one flip of a coin, is called a trial.
Missing Word
trial
A trial is one run of an experiment. The law of large numbers describes what happens to relative frequencies as the number of trials grows.
Category: Basic Terminology
Question 14
An event that cannot happen at all, such as rolling a 7 on a standard six-sided die, has probability 0 and is called impossible.
Missing Word
impossible
An impossible event cannot happen, so its probability is 0, the smallest value a probability can take. It contains none of the outcomes in the sample space.
Category: Basic Terminology
Question 15
In the formula P(A|B) = P(A AND B) / P(B), the probability of B appears in the denominator.
Missing Word
denominator
The probability of the given event is the denominator because the condition restricts attention to outcomes in B. Dividing by it rescales the probability of the overlap to that smaller sample space.
Category: Conditional Probability