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