Unit 5

Question 1

Random process

Answer 1

Any process determined by chance

Question 2

Trial

Answer 2

One repetition of a chance process

Question 3

Probability

Answer 3

A number between 0 and 1 that describes the proportion of times that outcome would occur in a very long series of repetitions

Question 4

Law of large numbers

Answer 4

If we observe many repetitions of a chance process the proportion of times an outcome occurs, Approaches its probability

Question 5

Understanding randomness

Answer 5

Randomness is only predictable in the long run, not the short run

Question 6

“Law of averages” myth

Answer 6

If it hasn’t happened in a long time it is due to happen

This is NOT TRUE

Question 7

Simulation

Answer 7

The imitation of some chance behavior

Based on a model that reflects the situation

Question 8

The simulation process

Answer 8

Describe how the chance behavior can be modeled

State what you will record at the end of each trial

Perform many trials

Use the results to answer the question of interest

Question 9

What # is considered statistically significant

Answer 9

5% or less

Question 10

Probability model

Answer 10

Description of some chance process that consists of:
A list of all possible outcomes, and the probability of each outcome

Question 11

Sample space

Answer 11

List of all possible outcomes

Question 12

Event

Answer 12

Any collection of outcomes from some chance process

Question 13

Probability models

Example

Answer 13

Roll a pair of dice

Let event A= sum is 5

4/36=0.111

Question 14

Probability of event A ( P(A) )

Answer 14

of outcomes in event A

/
Total # of outcomes in sample space

Question 15

Rules of a valid probability model

Answer 15

Prob of any event must be # between 0 and 1

All possible outcomes together must have probabilities that add up to 1

0 - prob an event does NOT occur
1 - prob it WILL occur

Question 16

Complement rule

Answer 16

P(A complement) = 1- P(A)

Question 17

Mutually exclusive

Answer 17

Events can NOT happen at the same time

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

If events A and B are mutually exclusive

Question 18

General addition rule

Answer 18

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

Finding P(A or B) when events are NOT mutually exclusive

Question 19

Complement, Intersection, Union

Answer 19

Page 11 has images of Complement, Intersection, and Union

Intersection - “And” n
Union - “Or” u

Question 20

Conditional Probability

Answer 20

The probability that one event happens given another event is known to have happened

P(A|B)

The vertical line means “given”

Question 21

Calculating conditional probability

Answer 21

P(A n B) / P(B) = P(A|B)

(A n B) —> both events
(B) —> given event

Question 22

Independent events

Answer 22

A and B are independent events if knowing whether one event has occurred or not does NOT change the probability that the other event occurs

If probabilities are = , events are independent
If probabilities are unequal, events are NOT independent

Question 23

The general multiplication rule

Answer 23

Probability both events A and B occur

P(A n B) = P(A) x P(B|A)

Question 24

Tree diagrams

Answer 24

Help us show the sample space of events that occur in sequence

All probs after the 1st event are conditional

Question 25

At least one rule

Answer 25

P(At least one) = 1 - P(None) VERY IMPORTANT SEE PAGE 18

Question 26

The multiplication rule for independent events

Answer 26

If A and B are Ind P(A n B) = P(A) x P(B)

Question 27

Standardized score (z-score)

Answer 27

The # of SD’s a data value is above or below the mean in a distribution Formula: Z=Value — Mean / Standard Deviation