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