law of large numbers
if we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value
probability
a number between 0 (never occurs) and 1 (always occurs) that describes the proportion of times the outcome would occur in a very long series of repetitions
ex: according to the a study, the probably that an adult eats breakfast is 0.61; explain what this means
if you asked MANY, MANY adults if they usually eat breakfast, about 61% would say yes (they do)
ex, cont: why doesn't .61 say that if 100 adults are chosen at random, EXACTLY 61 of them usually eat breakfast?
in a random sample of 100 adults, we would EXPECT ABOUT 61 would say "yes," however, the EXACT number will vary from sample to sample
this outcome is impossible and can never occur (number)
0
this outcome is certain and will occur on every trial (number)
1
this outcome is very unlikely, but will occur once in a while in a long sequence of trials (number)
0.01
this outcome will happen more often than not (number)
0.6
is there such thing as a "hot hand" in basketball? why/why not?
no; studies have shown that runs of baskets made/missed are no more frequent in basketball than would be expected if each shot was independent of the player's pervious shots (think of a coin toss)
simulation
the imitation of chance behavior, based on a model that accurately reflects the situation
simulation performing step #1
1) state: what is the ? of interest about some chance process?
simulation performing step #2
2) plan: describe how to use a chance device to imitate one repetition of the process; explain clearly how to identify the outcomes of the chance process and what variable to measure
simulation performing step #3
3) do: perform many repetitions of the simulation
simulation performing step #4
4) conclude: use the results of your simulation to answer the question of interest
sample space S of a chance process
the set of all possible out omws
probability model
a description of some chance process that consists of two parts: a sample space S and a probability for each outcome
event
any collection of outcomes from some chance process; a subset of the sample space; usually designated by capital letters (A, B, C, etc.)
two events are mutually exclusive (disjoint) if
they have no outcomes in common and, therefore, can never occur together
venn diagram
a diagram that uses circles to display elements of different sets. Overlapping circles show common elements.
general addition rule for two
if A and B are any two events resulting from some chance process, then:
P(A or B) = P(A) + P(B) - P(A and B)
U means:
union
upside down
U means
intersection
conditional probability
the probability that one event happens given that another event is already known to have happened
conditional probably ex:
suppose we know that event A has happened. the probability that event B happens GIVEN that event A has happened is denoted by:
P(B | A)
|" means:
given that" or "under the condition that