Probability and Uncertainty

Question 1

Probability let’s us quantify _______.

Answer 1

uncertainty

Question 2

Experiment: rolling a die
Sample space:
Event:

Answer 2

Sample space: 1,2,3,4,5,6
Event: even (2,4,6)

Question 3

What is a hit?

Answer 3

The occurrence of an event

Question 4

T or F
Probability can be any number.

Answer 4

False, probability is between 0 and 1.

Question 5

Mutually exclusive probabilities add up to _______.

Answer 5

1

Question 6

Classical approach

Answer 6

possible outcomes for E / total possible outcomes

Question 7

Relative frequency approach

Answer 7

of trials where E occurs / total # of trials

Question 8

Subjective approach

Answer 8

based on best guess, should be guided by existing information/research

Question 9

When do we use the subjective approach?

Answer 9

When trials are not possible

Question 10

Unions

Answer 10

A or B
disjunctions

Question 11

Intersections

Answer 11

A and B
conjunctions

Question 12

Marginal vs. Joint probability

Answer 12

marginal: simple
joint: 2+ variables

Question 13

Conditional probability

Answer 13

Probability of _______ based on _______.

Question 14

Independent events

Answer 14

the occurrence of one does not predict the occurrence of another

Question 15

Race and sex are independent events.

What is P(Female|Black)?

Answer 15

P(Female|Black) = P(Female)

Question 16

Dependent events

Answer 16

the occurrence of one helps predict the occurrence of another

Question 17

Gender and political party are dependent events in the House of Representatives.

T or F
P(Female|Democrat) = P(Female)

Answer 17

False, this would be true if they were independent.

Question 18

What is the probability rule for the conjunction of two independent events?

Answer 18

P(A and B) = P(A) x P(B)

Question 19

What is the probability rule for the conjunction of two dependent events?

Answer 19

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

Question 20

Does rolling a six on two dice at once represent independent or dependent events?

Answer 20

Independent

Question 21

Does drawing two spades from a deck of cards without replacing cards represent independent or dependent events?

Answer 21

Dependent

Question 22

What are two cautions in testing for independence?

Answer 22

1. Testing whether P(A|B) = P(B|A) does not test independence
2. You cannot assume independence

Question 23

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

Answer 23

False, for example, all pregnant people have a uterus but not all people with a uterus are pregnant.

Question 24

T or F
P(A|B) = P(B|A) when P(A) = P(B)

Answer 24

True

Question 25

Random variable

Answer 25

variable whose value is a numerical outcome of a random process

Question 26

The mean of X is sometimes called the _______ of X or the _______ of X, written as _______.

Answer 26

expected value, expectation, E(X)