Class 5 Spring 🌷

Question 1

What is the definition of probability?

Answer 1

A branch of pure mathematics about numerical description of the likelihood of an event

Question 2

What is the definition of statistics?

Answer 2

The collection, organization, displaying, analysis, interpretation, and presentation of data

Question 3

What does probability help quantify?

Answer 3

Uncertainty

Question 4

What is the difference between probability and statistics?

Answer 4

Probability is about chance; statistics is about data

Question 5

What is a simple (marginal) probability?

Answer 5

The probability of an event indicating how likely it is to occur

Question 6

What is the range of probability values?

Answer 6

0.0 to 1.0 (inclusively)

Question 7

What does a probability of 0.0 indicate?

Answer 7

Impossibility

Question 8

What does a probability of 1.0 indicate?

Answer 8

Certainty

Question 9

Define an event in probability.

Answer 9

A single or a set of outcomes from an experiment or process

Question 10

What is the probability of getting any 1 number with a fair die?

Answer 10

1/6

Question 11

What does the Law of Large Numbers (LLN) state?

Answer 11

As more observations are collected, the proportion of occurrences converges to the mathematical probability

Question 12

What is the common misunderstanding of the Law of Large Numbers?

Answer 12

That random processes compensate for past events (gambler’s fallacy)

Question 13

What are disjoint (mutually exclusive) outcomes?

Answer 13

Outcomes that cannot happen at the same time

Question 14

Give an example of a disjoint outcome.

Answer 14

A single coin toss cannot be both heads and tails

Question 15

What are non-disjoint outcomes?

Answer 15

Outcomes that can happen at the same time

Question 16

What is the addition rule for disjoint outcomes?

Answer 16

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

Question 17

What is the general addition rule for non-disjoint outcomes?

Answer 17

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

Question 18

Fill in the blank: The probability of an outcome is the proportion of times the outcome would occur if we observed the random process an _______ number of times.

Answer 18

infinite

Question 19

True or False: The probability of rolling a 1 or a 2 on a fair die is 1/3.

Answer 19

True

Question 20

What is the probability of selecting a diamond from a standard deck of cards?

Answer 20

13/52 = 0.250

Question 21

What is the probability of selecting a face card from a standard deck of cards?

Answer 21

12/52 = 0.231

Question 22

What is the probability of selecting a card that is both a diamond and a face card?

Answer 22

Calculated using the general addition rule, accounting for double counting

Question 23

What is a common application of probability in statistics?

Answer 23

Planning a sampling strategy to draw research samples from a larger population

Question 24

What is the probability of getting heads on the 11th toss after getting heads on the first 10 tosses?

Answer 24

0.5

Question 25

What is the effect of random sampling errors in statistics?

Answer 25

Separates the effect of random errors from the targeted effect of the treatment

Question 26

What does the notation for set theory specify?

Answer 26

Compound events

Question 27

What is the probability of it being a Monday?

Answer 27

P(Monday) = 52 / 365

Question 28

What is the probability of it being September?

Answer 28

P(September) = 30 / 365

Question 29

What is the probability of it being a Monday and in September?

Answer 29

P(Monday and September) = 4 / 365

Question 30

What is the probability of it being a Monday or September?

Answer 30

P(Monday or Sept) = 78 / 365 = 0.214 or 21.4%

Question 31

True or False: The sum of probabilities of two complementary events always adds up to 1.

Answer 31

True

Question 32

Define complementary events.

Answer 32

Two mutually exclusive events whose probabilities add up to 1.

Question 33

What is a sample space?

Answer 33

The collection of all possible outcomes of a trial.

Question 34

What are some examples of sample space?

Answer 34

* Winning or not winning a lottery ticket * Rolling a die {1, 2, 3, 4, 5, 6} * Being taller or shorter than someone {T, S} * Follower count growth scenarios {G, S, RS}

Question 35

Do the sum of probabilities of two disjoint events always add up to 1?

Answer 35

Not necessarily, there may be more than 2 events in the sample space.

Question 36

What is the definition of independent events?

Answer 36

Two processes are independent if knowing the outcome of one provides no useful information about the outcome of the other.

Question 37

Provide an example of independent events.

Answer 37

Flipping a coin and rolling a die.

Question 38

What is joint probability?

Answer 38

The probability of two events occurring simultaneously.

Question 39

What is conditional probability?

Answer 39

The probability of one event occurring in the presence of a second event.

Question 40

What does marginal probability refer to?

Answer 40

The probability of an event irrespective of the outcome of another variable.

Question 41

How can we find the joint probability of two dependent events?

Answer 41

Using conditional probability.

Question 42

What is the formula for calculating conditional probability?

Answer 42

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

Question 43

What does the notation P(A|B) represent?

Answer 43

The probability of event A occurring given that event B has already occurred.

Question 44

Calculate the conditional probability of rolling a die and getting a value less than 4, given that we know the value is an odd number.

Answer 44

P(value<4 | odd number) = 2/3 or ~0.667

Question 45

If two events are independent, what is the relationship between their probabilities?

Answer 45

P(A and B) = P(A) * P(B)

Question 46

If the conditional probability of two events is equal to the first event, what does this indicate?

Answer 46

The events are independent.

Question 47

What is the basic multiplication rule for independent events?

Answer 47

P(A and B) = P(A) * P(B)

Question 48

What is the basic multiplication rule for dependent events?

Answer 48

P(A and B) = P(A|B) * P(B)

Question 49

What is the probability that a patient relapsed in the given study?

Answer 49

P(relapsed) = 48 / 72 ~ 0.67

Question 50

What is the probability that a patient received the antidepressant and relapsed?

Answer 50

P(relapsed and desipramine) = 10 / 72 ~ 0.14

Question 51

Calculate P(relapse | desipramine).

Answer 51

P(relapse | desipramine) = 10 / 24 ~ 0.42

Question 52

What is the probability of receiving the antidepressant given that a patient relapsed?

Answer 52

P(desipramine | relapse) = 10 / 48 ~ 0.21

Question 53

What does it mean if the conditional probability of two events equals the first event?

Answer 53

They are independent events ## Footnote The inverse is also true.

Question 54

If two events are independent, what should knowing the outcome of one provide about the other?

Answer 54

No information

Question 55

What is the formula for the probability that the first die, X, is 1?

Answer 55

P(X = 1) = Favorable / All outcomes = 1/6

Question 56

What is the probability that the second die, Y, is 1 or 2?

Answer 56

P(Y = 1 or 2) = Favorable / All outcomes = 2/6

Question 57

What is the formula for conditional probability?

Answer 57

P(Y=1 or 2 | X=1) = P(Y=1 or 2 and X=1) / P(X=1)

Question 58

How does knowledge about event X affect the probability of event Y if they are independent?

Answer 58

It does not change it

Question 59

What happens to P(A and B) in the case of disjoint events?

Answer 59

It goes to 0

Question 60

What does P(A|B) simplify to in the case of independent events?

Answer 60

P(A)

Question 61

What is the probability that a randomly selected student is a social science major given that they are female?

Answer 61

P(SS | F) = 0.6

Question 62

What is the definition of probability?

Answer 62

The proportion of times an outcome would occur if observed infinitely

Question 63

What values can probability take?

Answer 63

Between 0.0 and 1.0 inclusively

Question 64

What percentage range can probability also be displayed as?

Answer 64

Between 0% and 100%

Question 65

What are marginal probabilities?

Answer 65

The probability of a single variable occurring

Question 66

What are joint probabilities?

Answer 66

Involve outcomes for two or more variables

Question 67

What is the addition rule for joint outcomes?

Answer 67

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

Question 68

What are the conditions for using the simple multiplication rule for joint probability with independent variables?

Answer 68

Events must happen at the same time and be independent

Question 69

What is the general multiplication rule for dependent variables?

Answer 69

P(A and B) = P(A|B) * P(B)

Question 70

What is the effect of random errors on variation in populations?

Answer 70

Effect of observable factors + Effect of unavoidable random errors

Question 71

True or False: Statistics is about data and the 'messy real' world.

Answer 71

True

Question 72

Fill in the blank: Probability is about _______ and the 'pure mathematics' world.

Answer 72

Chance

Question 73

What does P(SS | M) equal in the context of gender and major dependence?

Answer 73

0.6

Question 74

What is the implication if P(SS | F) = P(SS)?

Answer 74

Major does not depend on gender

Question 75

What percentage of all respondents said widespread gun ownership protects citizens?

Answer 75

58%

Question 76

What was the percentage of White respondents who said gun ownership protects citizens?

Answer 76

67%

Question 77

What was the percentage of Black respondents who said gun ownership protects citizens?

Answer 77

28%

Question 78

What was the percentage of Hispanic respondents who said gun ownership protects citizens?

Answer 78

64%

Question 79

What type of relationship is indicated if opinion on gun ownership and race ethnicity are not independent?

Answer 79

Dependent