intro to probability

p(E)

p(E)

n(E)/ n(S)

P(E’)

complementary event, 1-P(E)

independent events

events where the occurrence of one event does not affect the occurrence of the other event.

p(A&B) when independent

p(A) x p(B)

dependent events

events where the occurrence of one event does affect the occurrence of the other event (without replacement, etc)

p (A then B)

p(A) x p(B|A)

A U B

union of sets A and B, all elements belonging to A, B and A&B

A∩ B

all elements belonging only to both A & B

mutually exclusive/disjoint sets

no elements in common

addition law of probability

P(A U B) = P(A) + P(B) - P(A ∩ B)

if mutually exclusive, P(A U B) =

P(A U B) = P(A) + P(B)

P (A | B) =

P(A ∩ B) / p(B)

finding nth term

T r+1 = (nCr) x a^n-r x b^r (n= exponent r =term you’re tyring to find minus 1)

constant term

when exponent = 0

characteristics of a binomial probability

• 2 possible outcomes

• given number of trials

  • independent trials

discrete random variable

a variable that can only take on a countable number of distinct values. It cannot take on any value between these distinct values.

continuous random variable

has possible outcomes within an interval that need to be measured

number of times we expect event to occur =

n x p (n=number of trials) (p=probability)

binompdf

finding the possibility that x=r

binomcdf

finding the possibility that x< r (1- p = x>r)

mean of x

n x p

standard deviation of x

root of (np(1-p))

normalcdf

used for normal distribution problems

z score

how many standard deviations a point is away from the mean. z= x-μ/σ

finding p(z>a)

normalcdf (-E99, a)

finding p(z<a)

normalcdf (a, E99)

finding p(z>a>b)

normalcdf (a, b)

when given p=(x<k) = probability and told to solve for x

invnorm(probability)