AP Stats Unit 4 Part 1 Quiz

probability of an event =

(number of ways it can occur) / (total outcomes)

When is probability of an event used?

When all outcomes are EQUALLY LIKELY

3 properties of probability

1. it is alwasys between 0 - 1 (0% - 100%)

2. probabilities of all events add to 1 (100%)

3. complement rule: probability of an event A not happening

   • P(Ac) = 1-P(A)

1. complement rule equation

P(Ac) = 1-P(A)

Law of Large Numbers

after multiple trials, the relative frequency(proportion the event you are looking at occurs out of the total trials) of outcomes will approach the theoretical probability (probability of the event calculated)

Describe P(A) and P(B) (what do they mean)

all of P(A) —> probability of all occurrances of A; all of P(B) —> probability of all occurrances of B

Describe P(Ac) (what does it mean):

probability of not A; anything but A

Describe P(A∪B):

OR symbol; union; one the other, or both

Describe P(A∩B)

AND symbol; intersection; A and B

P(A∪B); Simple addition rule for NOT mutually exclusive events

• P(A∪B) = P(A) + P(B) - P(A∩B)

• avoids double counting(must subtract the overlap)

mutually exclusive events

when events have no intersection (they both cannot occur at the same time)

P(A∪B); Simple addition rule for mutually exclusive events

• P(A∪B) = P(A) + P(B)

• there is no overlap bc mutually exclusive, so no need to subtract

condition

a “given” in a problem, P(A|B) is the probability of A given B has occurred

Conditional probability formula (general, does not take into account dependent vs. independent events)

P(A|B) = P(A∩B) / P(B)

• finding the probability of the “overlap” between A and B

given means … (in calculations)

divide by the given (event/given)

independence(describe)

two events (A and B) are independent if the known outcome of one event DOES NOT AFFECT the outcome/probability of the other event

equation to prove if events are independent

P(A|B) = P(A) or P(B|A) = P(B)

P(A∩B); Formal multiplication rule for dependent events

P(A∩B) = P(A) * P(B|A)

P(A∩B); formal multiplication rule for independent events

P(A∩B) = P(A) * P(B)

mutually exclusive events:

not independent; knowing that one event occurs affects the probability of the other event (lowers it to 0)

intuitive multiplication rule (general rule, does not take other factors into account)

AND means multiply (will need to account for dependent events)

intuitive addition rule (general rule, does not take other factors into account)

OR means add (will need to account for double counting

If stuck for probability…

draw first (venn diagram, table, or tree)

probability does not ______ because of previous events; there is an _______ ______ chance each trial

change; equally likely

the idea of probability is that _________ is predictable in the ________

randomness; long run

how to perform a simulation

1. 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 tiral

   • STATE(context)

   • PLAN

2. Do: Perform many trials

3. Conclude: Use the results of your simulation to answer the question of interest

steps for PLAN part of simulation

• Assign: assign digits to represent different events being observed

• Stopping rule: state when to stop selecting digits

  • include if selecting with or without replacement

  • if using replacement, include if using repeats or not

• Response variable: describe what trials are counted as successes and what trials are counted as fails

all labels (digit assignments for events) must be..

the same length (ex if looking at 2 digit numbers, use 00-91 not 0-91)

when sampling without replacement for simulation must state…

if repeated numbers should be ignored or if different numbers should be selected