AP Stat Unit 2 Quiz

short run probaiblity is

unpredictable

long run probability is

regular and predictable

Law of Large Numbers

simulated probabilities tend to get closer to the true probability as the number of trials increases

Guideline for interpreting probability

After Blank (how every many spins/ flips etc) the percent of times CONEXT approaches %%% in the long run

simulation

a way to model random events such that simulated outcomes closely watch the read world outcomes

statistically significant

if the number is less then 5%- means that unlikely for this event to happen purely by chance

sample space

list of all possible outcomes

P(E)=

# of outcomes/ total # of outcomes in sample space

compliment rule

P(A^C) =1-P(A)

if you have P(A∩B) what do you do

multiply P(A) x P(B)

If you have P(A U B) what do you do

add P(A) x P(B)

mutually exclusive

two events that can never occur together at the same time

Addition

For P( A or B)=P(A) + P(B) - P(A and B)

The probability of any outcome or event from a random process is a number between

0 and 1 that describes the proportion of times the outcome or event would occur in a very long series of trials

how to perform a simulation to estimate the probability of an outcome or event

Describe how to set up and use a random process to perform one trial of the simulation. Identify what you will record at the end of each trial.

Perform many trials.

Use the results of your simulation to answer the question about the outcome or event of interest.

outcome

result of one trial

event

collection of outcomes

how to design a simulation

1. assign

2. describe one trial

3. repeat many times

4. conclude

probability of the sample space is equal to

1

a zero probability is

impossible

compliment

the probability of NOT E = 1- probability of E

Mutually Exclusive

can not happen at the same time (justify that a and b can both not happen at the same time)

In a venn diagram if there is no mutually exclusive events, do the ciricles overlap

no

conditional probability

p(A given B already happening)= Probability (a and b occuring at the same time/ Probability of B)

independent events

knowing one happened doesn’t change the probability of the other

two event are independent if

P(A|B) = P(A)

union meaning

A OR B HAPPENIGN

All probabilities are between

0-1 or0%-100%

interpreting P(A)= 0.25

if this process were repeated a larger number of times, about 25% of the repetitions would result in A

Estimate the P(Event)

number of times the event occured/ number of trials

Random outcomes have no…

memories- past results dont change the probability of the next outcome

If a question asks you to use results to estimate probability do

the number of times that thing occured/ the number of trials completed

P(at least 1)

1-P(none)

if A and b are not mutually exclusive, then use the

general addition rule

How to tell if an event is mutually exclusive

find P(A and B) if it is = 0, then it is mutually exclusive if not, then it is not mutually exclusive

when running a single trial, you want to get the result that

simulates the same number of trials completed in the actual trial and with the same percent as the probability

Whenever a question asks you to find P(A orB) what must you look for first

whether or not the events are mutually exclusive!!! if they are not, then you must use the general addition rule

if a question says what is the probability of both candies being one color or another color what should you do

P(A and B) P(A) X P(B)

to find the probability of an event happening with a given number of trials multiply

the number of trials x the predicted probability