8.1 - Probability Foundations

Trial

one run of the event

Outcome

any one result from a scenario

sample space

all of the possible outcomes

ex: flipping a coin to get Heads or Tails

Event

verb + outcome flipping a coin to get a H

Probability formula

P(A) = n(a)/n(U)

n(a): how many we want

n(U): all possible options

x’ means not x

complements formula

P(A’) = 1 - P(A)

P(A) + P(A’) = 1

experimental probability

prob based on running an experiment

theoretical probability

prob. based on theory/on paper

relative frequency

number of times the event occurs/number of trials

larger comparable samples generally give reliable or unreliable estimates?

they give more stable estimates

an estimate need not improve after every new trial

how can I improve the estimate

combine the numerators and the denominators of each event/batch

expected number

np (number of trials x probability of the event)

expectation predicts an average count across repetitions

• doesn’t need to be a whole number

• not guaranteed based on one set of trials