AP Statistics - Unit 4: Probability (Chapter 13 - 15)

aAAAaaAAAaaaAAaAaAAaaAAAaaaAAaAaaaAAAaaAa

random

we know what could happen, but you don’t know what will happen

trial

one attempt at a random phenomenon

outcome

the result of a trial

sample space

set of all possible outcomes (S = {1, 2, 3, …})

the sum of all probabilities equals 1

probability of an event

P(A) = (number of favored outcomes) / (number of possible outcomes)

always between 0 and 1 (100%)

complement of A (A’)

P(not A) = 1 - P(A)

mutually exclusive (disjoint)

events that don’t share any outcomes in common

addition rule

mutually exclusive: P(AuB) = P(A) + P(B)

general: P(AuB) = P(A) + P(B) - P(AnB)

union (u)

“or” A or B or both

intersection (n)

“and” both A and B

multiplication rule

multiply the probabilities of two events if there are multiple things happening

independence

events A and B are independent if P(B|A) = P(B)

conditional probability

P(A|B) = P(AnB) / P(B)

| = “given”

tree diagram

a way of showing all possible outcomes and their probabilities, works well with conditional probability

probability of “at least one”

probability of not 0

P(not 0) = 1 - P(0)

law of averages

the probability of something occurring increases if you are further from the average (due for a…)

this rule is false

law of large numbers

as we repeat a random process over and over, the true probability will emerge

random variable (X)

a number based on a random event

expected value of a random variable E(X)

Σ[x * P(x)]

standard deviation of a random variable SD(X)

sqrt {Σ[(x - x-bar)^2 * P(x)]}

probability model

outcome, x, P(X = x)

shifting a random variable

add/subtract from the mean, does not affect standard deviation

rescaling a random variable

multiply mean/standard deviation by the factor

adding two random variables

E(X + Y) = E(X) + E(Y)

SD(X + Y) = sqrt [SD(X)^2 + SD(Y)^2]

subtracting two random variables

E(X - Y) = E(X) - E(Y)

SD(X - Y) = sqrt [SD(X)^2 + SD(Y)^2]

summing a series

E(X1, X2…Xn) = n * E(X)

SD (X1, X2…Xn) = sqrt [n * SD(X)^2]

using a normal model to find probability

find the expected value and standard deviation, find the z-score, use normal cdf