Glossary
Complement (of an event)
An event consisting of all outcomes in the sample space that are not part of the original event. Its probability is 1 minus the probability of the original event.
Example:
If the probability of a student passing a test is 0.85, then the complement is the student failing the test, with a probability of 1 - 0.85 = 0.15.
Contextual Interpretation of Probability
The ability to explain the meaning of a calculated probability in the specific real-world scenario of the problem, often using phrases like 'randomly selected' or 'chance.'
Example:
If the probability of a randomly selected customer buying coffee is 0.6, a good contextual interpretation of probability would be: 'There is a 60% chance that a randomly selected customer will purchase coffee.'
Equally Likely Outcomes
Outcomes in a sample space that each have the same chance of occurring, allowing probability to be calculated as the ratio of favorable outcomes to total outcomes.
Example:
When rolling a fair six-sided die, each number from 1 to 6 represents an equally likely outcome, each with a probability of 1/6.
Probability (of an outcome)
A numerical value between 0 and 1 that quantifies the likelihood of a specific outcome occurring.
Example:
If you draw a card from a standard deck, the probability of drawing the Ace of Spades is 1/52.
Probability Model
A mathematical description of a random process, consisting of a sample space and the probability of each outcome.
Example:
When analyzing a spinner with four equal sections (red, blue, green, yellow), the probability model includes the list {red, blue, green, yellow} and the probability 0.25 for each color.
Probability Range
The principle that all probabilities must be a value between 0 and 1, inclusive, where 0 indicates impossibility and 1 indicates certainty.
Example:
If a student calculates a probability of 1.2 for an event, they know they've made an error because the probability range dictates the value must be between 0 and 1.
Sample Space
The set of all possible outcomes of a random phenomenon.
Example:
For choosing a day of the week, the sample space is {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}.
Sum of All Probabilities
The rule stating that the probabilities of all possible outcomes in a sample space must add up to exactly 1.
Example:
If the probabilities of rain, snow, or clear skies are 0.3, 0.2, and 0.5 respectively, their sum of all probabilities is 0.3 + 0.2 + 0.5 = 1, covering all weather possibilities.