Semester 2 Math Formulas/Theorms

Theoretical Probability (LT #14)

• the expected value

• # of outcomes in event _ / total # of outcomes

Experimental Probability (LT #14)

• the actual value

• # of trials where _ occured / total # of trials

Intersection (A n B) (LT #14)

• when two events occur simultaneously at the same time

• P(A n B) = P(A) • P(B | A) or P(B) • P(A | B)

• if mutually exclusive (A n B) = 0

Mutually Exclusive (LT #14)

• events with NO common outcomes

• when P(A n B) = 0

Union (A u B) (LT #14)

• P(A) + P(B) — P(A n B)

Conditional Probability P(B | A) (LT #14)

• (A | B) = P(A n B) / P(B)

Independent Events (LT #14)

• P(A n B) = P(A) • P(B)

• OR P(A) = P(A | B)

• Both sides of equation must be the same in order to be independent IF NOT events are associated

Fundamental Counting Principle (LT #15)

if there are n amount of items there are m1 ways to organize the first item, m2 ways for the second, etc.

Permutation (LT #15)

• order DOES matter

nPr = n! / (n - r)!

• n = total # of available items

• r = chosen/selected items

Combination (LT #15)

• order DOES NOT matter

nCr = n! / (n - r)!r! = (n/r)

• n = total # of available items

• r = chosen/selected items

Permutation (with Repetition) (LT #15)

n! / r1!…r2!…etc.

• n = # of total objects

• r = the object repeated

# of permutations of n distinct objects if an object is repeated r1 times, another is repeated r2 times and so on is...

• count how many times a letter is repeated (i.e. if e is repeated 3 times in the word repeated) then that number will become a factorial on the bottom (i.e. r)

Specific Outcomes Probability (LT #15)

if a specific variable is included/known (ex. 2 friends will receive invitation) then use

# of outcomes where ___ is included / # of total possible outcomes

• should use even on poker hands! (sometimes)

Z-score

z = x-u / o

• x = data pont (value)

• u = mean of data

• o = standard deviation

• once z is found look at the table

Experiment

IMPOSING treatments on a group of assigned subjects in order to see different responses to the treatments

Observational Study

Observed information is used to record values of variables for

members of a sample

• no interactions

Survey

A type of observational study that gathers data by asking

people a number of questions

Sample Survey

A type of observational study that gathers data by asking

a sample of people to answer a number of questions

Population Proportion

proportion of a group of people

Sample Proportion

proportion of the sample (mean/avg.)

Margin of Error for Population Proportion

1.96 x sqrt p^(1-p^) / n

• p^ = sample proportion / total sample

• n = total sample

Margin of Error for Population Mean

1.96 x s (SD) / sqrt of n

• SD = standard deviation

• z-score of 1.96

• n = data value (total sample)

Confidence Interval for Population Proportion

p^ ± M (moe)

• p^ = population proportion

• M = margin of error

Confidence Interval fro Population Mean

x̄ ± M (moe)

• x̄ = population mean

• M = margin of error