Chapter 6 - Probability & Simulation: The Study Of Randomness

Front 1

Addition Rule for Disjoint Events

Back 1

If events A, B, and C are disjoint in the sense that no two have any outcomes in common, then
P(A or B or C)=P(A)+P(B)+P(C)

Hint 1

Front 2

General Addition Rule for Unions of Two Events

Back 2

For any two events A and B,
P(A or B)=P(A)+P(B)-P(A and B)

Hint 2

Front 3

Simulation

Back 3

Imitation of chance behavior, based on a moedl that accurately reflects the phenomenon under consideration

Front 4

Randint Function

Back 4

randint(x,y,z)
x=minimum
y=maximum
z=number of digits to generate

Front 5

Simulation Steps

Back 5

State problem or describe random phenomenon
state assumptions
assign digits
simulate many repetitions
state conclusions

Front 6

Empirical

Back 6

Based on observation, not theory

Front 7

Probability Models

Back 7

Sample space S of a random phenomenon is set of all possible outomes

event is any outcome or set of outcomes of a random phenomenon

probability model is mathematical description of a random phenomenon, consisting of a sample space and a way of assigning probabilities to events

Front 8

Tree Diagram

Back 8

A handy way to depict all possible outcomes

Front 9

Multiplication Principle

Back 9

if you can do something n ways and another m ways, the total number of ways to do both is n x m

Front 10

Sampling with replacement

Back 10

Put the things back after drawing

Front 11

Sampling without replacement

Back 11

Not putting things back after drawing them

Front 12

probability rules

Back 12

any probability is between 0 and 1
the sum of all probablities of all possible outcomes must equal 1
if 2 events have no outcomes in common, the probability that one or the other occurs is the sum of the two individuals
the probability that an event does not happen is 1 minus the probability that the event does occur

Front 13

Mickey Rat

Back 13

RATS

Hint 13

Front 14

Venn Diagram

Back 14

diagram to find probability of union of two events or joint probability

Hint 14

Front 15

Disjoint events

Back 15

probability of A and B is 0

Front 16

Conditional Probability

Back 16

Front 17

Complement (A^c)

Back 17

i.e. complement of Event A is all outcomes that are not in A

Front 18

Random Phenomenon

Back 18

Outcomes that we cannot predict but that nonetheless have a regular distribution in very many repetitions.

Front 19

Total Probability

Back 19

All of the probabilities must add up to 1.

Hint 19

P(S) = 1

Front 20

Joint Probability

Back 20

The probability of two events occurring together.

Hint 20