Probability

an identification number consist of 4 digits. Each digit can be 0-9 and each digit can be repeated. what is the probability of randomly generating your identification number?

10•10•10•10=10000 probability- 1/10000~0.0001

simple event

an event that consists of a single outcome

non simple event

an event that consists of more than one outcome

law of large numbers

as an experiment is repeated over and over, the empirical probability of an event approaches the theoretical (actual) probability of the event example: you may get 7 or 8 heads if you flip a coin 10 times, however the more times you flip the coin, the closer the percentage of heads to 50%

empirical probability

based on observations obtained from probability experiments example: according to Company Records, the probability that a washing machine will need repairs during a 6 year period is 0.10

event

consists of one or more outcomes and is a subset of the sample space

fundamental counting principle definition and equation

definition: If one event can occur in m ways and a second event can occur in n ways, the number of ways the two events can occur in sequence is m*n formula: (amount of times one event can occur)*(amount of time another event can occur) or m*n examples: you flip a fair coin three times and record the outcomes for heads and tails. 2•2•2•=8 (a coin has 2 outcomes and you flip it 3 times) In how many ways can a six-question true-false quiz be answered? 6•2=12 (a true false question has 2 outcomes and you have 6 of them)

classical probability

each outcome in a sample space is equally likely example: rolling a dice, flipping a coin

subjective probability

intuition, educated guesses, and estimates example: a doctor may feel a patient has a 90% chance of a full recovery

independent events definition and formula

the occurrence of one of the events does not affect the probability of the occurrence of the other event formula:

conditional probability

the probability of an event occurring given that another even has already occurred example:

outcome

the result of a single trial in a probability experiment

complimentary events

the set of all outcomes in a sample space that are not including the positive event example: 40% of students got above a 90% on a test 40%=.4 1-.4= .6 60% of students did not get a 90% or above on a test 60% (or .6) is the compliment to 40% (.4)

sample space

the set of all possible outcomes of a probability experiment