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Probability formula sheet

14 formulas ยท what each one means ยท a free lesson for each

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steplyclass.com/formula-sheets/probability/ ยท free, step-by-step lessons for every formula

Counting

Counting principle
m ร— n
m ways for the first choice and n for the second: m ร— n ways together.Lesson: Counting choices โ†’
Factorial
n! = n ร— (n โˆ’ 1) ร— โ€ฆ ร— 2 ร— 1
0! = 1.Lesson: Factorials โ†’
Permutations (order matters)
nPr = n!(n โˆ’ r)!
Lesson: Permutations โ†’
Combinations (order does not matter)
nCr = n!r!(n โˆ’ r)!
Lesson: Combinations โ†’

Probability rules

Probability
P(A) = number of ways A can happentotal number of outcomes
Between 0 (never) and 1 (always).Lesson: Probability โ†’
Complement
P(not A) = 1 โˆ’ P(A)
Lesson: Probability โ†’
Odds
odds for = favorable : unfavorable
Lesson: Odds โ†’
Experimental probability
times it happenedtimes tried
Lesson: Experimental probability โ†’
Or
P(A or B) = P(A) + P(B) โˆ’ P(A and B)
Take away the overlap, so it is not counted twice.Lesson: Probability with or โ†’
And (independent)
P(A and B) = P(A) ร— P(B)
When one does not change the other.Lesson: Probability with and โ†’
And (dependent)
P(A and B) = P(A) ร— P(B | A)
Lesson: Probability with and โ†’
Conditional probability
P(B | A) = P(A and B)P(A)
The chance of B when A has happened.Lesson: Conditional probability โ†’
Expected value
E = ฮฃ x P(x)
Each value times its probability, added.Lesson: Expected value โ†’
Binomial probability
P(x) = nCx px qnโˆ’x, q = 1 โˆ’ p
x successes in n tries.Lesson: Binomial probability โ†’

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