test #3- Probabilities Flashcards
what is an event
any collection off results or outcomes of a procedure
what is a simple event
an outcome that cannot be further broken down into simpler components
what is a sample space
it consists of all possible simple events
how do you calculate the number of times an event occurs
(#times event A occurs) x (# of times the procedure is repeated)
what are complementary events
finding the probability that an event does not occur
what is the complement of an event
everything but that event (A’)
what are compound events
any event combining two or more simple events
P(A or B)=
P(A) + P(B) - P(A and B)
What are independent invents (with replacement)
when the occurence of one does not affect the occurence of the other
what are dependent events (without replacement)
when the occurence of one event affects the occurence of the other
p(A and B)=
P(A) x P(B)
what is conditional probability
when an event’s probability is obtained with the additional information that some other has already occurred (on that condition that)
P(A|B)=
P(A intersect B) / P(A)
what are permutations
when different sequences of the same items are considered unique
what are combinations
when different sequences of the same items are not considered unique
fundamental counting rule;
(# of ways the first event occurs) x (# of ways the 2dn event occurs) (ex:how many possible codes exists with letters/numbers)
Factorial rule;
n! ex: (5 students and 5 seats how many permutations?)
permutation rule (when all items are different)
number of permutations when “n” items are available but only “r” are selected ex(5 students but 3 chairs)
permutation rule (when some items are the same)
number of permutations when “n” items are available and selected but some items are identical
combinations rule
number of different combinations when “n” items are available but only “r” are selected.
what is a random variable
a variable that has a single probability for each value of x
what is a discrete random variable
random variable with finite values
what is a continuous random variable
random variable with infinitely many values
what is a probability distribution
a description that gives the probability for each value of x of the random variable
what are the three requirements for a probability distribution
1- there is a numerical random variable and its x values have a corresponding probability
2- Ep(x)=1
3- p(x) is higher than zero but smaller than 1
what is the range rule of thumb
the vast majority of values lies within 2 standard deviations of the mean
what is binomial probability distribution
it allows us deal with situations in which outcomes belong to one of two categories; success or failure
what are the four requirements for binomial probability distribution
1- the procedure has a fixed number of trials
2-the trials must be independent
3- each trial falls into either success or failure
4- the probability of success remains the same in all trials
