Studied by 6 peoplemutually exclusive
Events that cannot occur at the same time.
he intersection or joint probability of two events, denoted by P(A and B) where A and B are two events
the probability of both events occurring simultaneously
Addition Rule of Probability P(A or B)
P(A or B) = P(A) + P(B) - P(AB) subtract overlap
independent events
The outcome of one event does not affect the outcome of the second event
if event a happens changes probability of b happening it is...
NOT Independent
P(A and B)= P(A) x P(B | A)
Formula for 'removed without replacement' (probability) Not independent
If two events are independent, then
the product of their probabilities gives their intersection. P(A and B)= P(A) x P (B)
mutually exlusive events
addition rule P(A or B)= A+ B- (A and B)
If not mutually exclusive... ( No overlap and cannot happen at same time)
P(A or B) = P(A) + P(B) - which is 0 !! P(A and B)
If events are independent (one does not affect other) then
P( A and B)= P(A) x P (B)
If events are not independent...
P (A and B) = P (A) x P (B|A)
when to use tree diagram
if P(A) (marginal), P(B | A) (conditional), etc. two back to back events happening
marginal frequency
The sums of the rows and columns in a two-way table
P( A | B) : find denominator first
then figure out how much also get A but of denominator too
AP Exam tips
Create model like tree diagram or two way table for story probability problems
Calculate all probabilities in diagrams even if you don't need to solve problem
Formulas should be last resort for probability problems
Binomial Distribution
a frequency distribution of the possible number of successful outcomes in a given number of trials in each of which there is the same probability of success.
What must be true of binomial distribution?
BINS B- Binary (number success/ failures ONLY TWO OPTIONS I- Independent N- n sample certain amount of trials S- same probability for every amount shot
anytime describing distribution use, socs which is
shape outlier center spread
Central Limit Theorem????????????
As the size n of a simple random sample increases, the shape of the sampling distribution of x̄ tends toward being normally distributed.
Large Counts Condition???????
using normal approximation when np>=10 and n(1-p)>=10 n(successes)= see if its greater than 10 n( failures)= see if its greater than 10 thats how you know shape is approx. normal
where to find center and spread of binomial distribution?
formula sheet
binomialpdf(100, 0.85, 80) EXACTLY 80 SHOTS
(n (trials), probability of success, amount of values we need
at least 80 shots= binomialCDF or cumulative binomailcdf (100, .85, 80, 100)
(n, probability of success, lower bound, upper bound)
AP Exam Tips binomial functions
any bionomial function shape,. center, spread formula sheet
when is binomial spread appx. normal?
np greater than or equal to 10 AND n(1-p) greater or equal to 10 other words probability of successes AND failures are greater than 10
if you use binomial calculator functions you must?
specify that the diostribution is binomial along with clearly identifying p and n
multiplication rule
A rule of probability stating that the probability of two or more independent events occurring together can be determined by multiplying their individual probabilities.
Note
Flashcard