AP Statistics Test 3

Time series plot

Plotting cumulative results in a sequence

Law of Large Numbers

The larger the number of trials/simulations, the closer the result will be to the true probability

If probability is 0…

It means it is impossible

If probability is 1…

This outcome is certain. It will occur on every trial

If probability is 0.001…

This outcome is very unlikely, but it will occur once in a while in a long sequence of trials.

If the probability is 0.6…

This outcome will occur more often than not, but doesn’t occur almost every time.

Sample space

Representation of all possible outcomes

Complement

The opposite thing happening

P(E^c)=P(E)

P(E not happening) = 1 - P(E)

U=

Or

P(E) =

# of outcomes that E has/total in sample space

P(A and B) =

P(A) x P(B), only if A & B are independent

P(A or B) =

P(A) + P(B), only if A & B are mutually exclusive → can’t both happen

P(A U B) =

P(A) + P(B), only works if mutually exclusive

OR

inclusive: event A happens, event B happens, or BOTH happen

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

Venn Diagram Area: Includes circles A, B, and the middle intersection

XOR

Exclusive OR: event A happens or event B happens, but NOT BOTH

P(A xor B) = P(A) + P(B) - 2P(A and B)

Venn Diagram Area: includes circles A and B, but LEAVES OUT middle intersection

Complement

P(either^c) = 1 - P(Either)

Why does P(X or Y) not equal P(X) + P(Y)?

Because if there is an overlap, it must be subtracted

Events are independent if:

P(A) = P(A|B) = P(A|B^c)

| =

“Given”

C =

The complement

Two events are independent if…

Knowing whether or not one event has occurred does not change the probability that the other event will occur.

Events are not independent if…

The percentages are different.