Glossary
Addition Rule (for 'OR')
Used to find the probability of either event A or event B occurring: P(A or B) = P(A) + P(B) - P(A and B).
Example:
To find the probability of drawing a king or a heart from a deck, you'd use the addition rule (for 'OR'), accounting for the king of hearts overlap.
Calculating Probability
The method of determining the likelihood of an event by dividing the number of favorable outcomes by the total number of possible outcomes, assuming outcomes are equally likely.
Example:
To find the calculating probability of drawing a red card from a standard deck, you'd divide 26 (favorable) by 52 (total), resulting in 0.5.
Complement of an Event (A')
All outcomes in the sample space that are not part of a given event A. Its probability is P(A') = 1 - P(A).
Example:
If event A is rolling a 6 on a die, the complement of an event (A') is rolling any number other than 6.
Compound Event
An event that consists of two or more simple events combined.
Example:
Flipping a coin and getting heads, and then rolling a die and getting an even number, is a compound event.
Conditional Probability
The probability of an event A occurring given that another event B has already occurred, denoted as P(A|B) = P(A and B) / P(B).
Example:
The conditional probability of a student passing a test, given that they studied for more than 5 hours, would be calculated using this concept.
Event
A specific outcome or a collection of outcomes from a sample space that you are interested in.
Example:
If you roll a die, getting an even number (2, 4, or 6) is an event.
Law of Large Numbers
A principle stating that as the number of trials in a random experiment increases, the relative frequency of an event tends to get closer to its true theoretical probability.
Example:
The more times you flip a fair coin, the closer the relative frequency of heads will get to 0.5, illustrating the Law of Large Numbers.
Measurement Error
The difference between a measured value and the true value, which can occur due to inaccuracies in instruments or procedures.
Example:
If a scale consistently reads 1 pound heavier than the actual weight, this is a form of measurement error.
Multiplication Rule (for 'AND', Dependent Events)
Used to find the probability of two dependent events A and B both occurring: P(A and B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given A.
Example:
To find the probability of drawing a red card, and then drawing another red card without replacement, you'd use the multiplication rule (for 'AND', dependent events).
Multiplication Rule (for 'AND', Independent Events)
Used to find the probability of two independent events A and B both occurring: P(A and B) = P(A) × P(B).
Example:
The multiplication rule (for 'AND', independent events) helps calculate the probability of flipping a coin and getting heads, and then rolling a die and getting a 3.
Probability
The numerical measure of the likelihood that an event will occur, expressed as a value between 0 (impossible) and 1 (certain).
Example:
The probability of flipping a fair coin and getting heads is 0.5.
Relative Frequency
An estimate of probability based on observed data, calculated as the number of times an event occurs divided by the total number of trials.
Example:
If a basketball player makes 7 out of 10 free throws in practice, their relative frequency of making a free throw is 0.7.
Sample Size
The number of observations or individuals included in a statistical sample, which affects the reliability of probability estimates.
Example:
A survey of 10,000 people has a larger and generally more reliable sample size than a survey of 100 people.
Sample Space
The set of all possible outcomes of a random experiment.
Example:
When rolling a standard six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
Sampling Bias
A systematic error in the selection of a sample that causes it to not be representative of the population, leading to inaccurate conclusions.
Example:
Surveying only students in advanced math classes to gauge overall student interest in math could introduce sampling bias.
Simple Event
An event that consists of only one outcome from the sample space.
Example:
Rolling a 7 on a 10-sided die is a simple event.