Basic probability rules, permutations, and combinations for middle and high school math, distinct from the statistical-inference focus of AP Statistics.
36 cards · basic cards · AI-written, checked twice. Edit anything.
- What is the probability of an event?
- The ratio of favorable outcomes to total possible outcomes, assuming all outcomes are equally likely.
- What is the range of a probability value?
- Between 0 and 1, inclusive. P(event) can equal 0 (impossible) or 1 (certain).
- What does the complement of an event mean?
- The complement of event A is all outcomes that are not in A, denoted A' or A^c.
- State the complement rule for probability.
- P(A') = 1 - P(A), where A' is the complement of event A.
- When are two events mutually exclusive?
- When they cannot occur at the same time; they have no outcomes in common.
- State the addition rule for mutually exclusive events.
- P(A or B) = P(A) + P(B), when A and B cannot occur together.
- State the general addition rule for any two events.
- P(A or B) = P(A) + P(B) - P(A and B).
- When are two events independent?
- When the occurrence of one event does not affect the probability of the other.
- State the multiplication rule for independent events.
- P(A and B) = P(A) x P(B), when A and B are independent.
- Define conditional probability.
- The probability of an event A occurring given that event B has already occurred, denoted P(A|B).
- State the conditional probability formula.
- P(A|B) = P(A and B) / P(B), provided P(B) > 0.
- Define factorial notation.
- n! (n factorial) is the product of all positive integers from 1 to n. Example: 5! = 5 x 4 x 3 x 2 x 1 = 120.
- What is 0! (zero factorial)?
- By definition, 0! = 1.
- Define a permutation.
- An arrangement of objects where order matters. The number of permutations of n objects taken r at a time is nPr.
- State the permutation formula.
- nPr = n! / (n-r)!, where n is the total number of objects and r is the number being arranged.