probability Flashcards
what is probability?
the likelihood or chance of an event occurring (numerical measure of how likely an event will occur)
what is the purpose of probability?
business statistics apply mathematical formulas or models to business information in an attempt to determine the probability of success relating to an opportunity
(will new delivery service improve customer satisfaction)
stats used to measure this probability
how is probability used in inferential statistics?
predict the probability that the whole sample will be the same as the population
what is the numerical value of probability?
range from 0 - 1
percentages or odds
what ate the 3 sources of probability?
- subjective
- classical (theoretical)
- empirical (statistical)
what is subjective probability?
- lilihood of particular event assigned by individual based on whatever info is available
- if little or no info, prob is based on subjectivity
- soley based on intuition
(football predictions)
what is classical / theoretical probability?
- all outcomes are equally likely
- probability is a logical thing
what is the formula for classical / theoretical prob?
no. of favourable outcomes / no. of possible outcomes
roll of a dice = 1/6
what is empirical (statistical) prob?
- based on experiments
- relative freqenecuy
= proportion of times the outcome has occurred over many repetitions - probability has come from historical records?
= frequency probability
example rainy days
169/365 = 0.43 x 100 = 43%
- assumption that it doesn’t deviate from past outcomes
what is an experiment?
action / process with a well defined set of outcomes on a single repetition (trial) only one possible outcome occurs
what is a sample space?
set of all possible outcomes
what is an element?
specific outcome (sample point)
what is an event?
subset to sample space, it may be specific outcome or combination of outcomes
what is th eporbabaility of an event?
sum of all probabilities of all elements that make up every
what is combining events?
rules of probability
- addition rules
- multiplication rules
one event with another
what is meant by general and specific?
wether two events are indpeneet of eahcother
what is the specific event for addition rule? ‘or’
indenpenedant of other event (don’t happen at same time, not influenced)
P(A or B) = P(A) +P(B)
what is the general rule for addition rule?
not indépendant
P(A or B) = P(A) +P(B) - P(A and B)
what is the specific rule for multiplication?
‘and’
P(A and B) = P(A) x P(B)
what is the general rule for the multiplication rule?
e.g. if you pick a card out of a pack of a cards this will have an event on the likelihood of picking other cards
P(A and B) = P(A) x P(B | A) - given that A has already happened
e.g. 4 / 52 then one card picked so it becomes 4 / 51
what are expected values?
we can calculate them based on probability
the return you can expect for some kind of outcome
what is the formula for expected value?
sum of [ P(outcome) x result of outcome ]
what is porbabailty distribution?
statistical model that shows the possible outcomes of a particular event as well as statistcial likelihood of each event
what is discrete probability distribution?
finite no. of values only take on certain no. of values
X can take on values from 1-6 with probabilities of 1-6
what is continuous probability distribution?
- as the number of trials increases, bar charts become more of a smoother curve
- variable X can assume a continuous set of variable
total area of relative frequency polygon = 1
(probability function density)
what is normal distribution?
one of the most important examples of continuous probability dstrbtion
most common
why would you transform normal distribution into standard normal distraction?
because every normal dis has a diff mean and SD whereas SND has a mean of 0 and SD of 1
