Chapter 3

Question 1

What do PDF and CDF tables share in terms of characteristics?

Answer 1

Identical characteristics

Question 2

What do both PDF and CDF values sum up to?

Answer 2

One

Question 3

Is summing PDF and CDF values useful or meaningful?

Answer 3

No

Question 4

In what context is the Z-score placed?

Answer 4

Context of the CDF

Question 5

How is the Z-score defined?

Answer 5

CDF probability that X is less than or equal to a specific value

Question 6

What example value was mentioned in relation to Z-scores?

Answer 6

18

Question 7

What is crucial for accurate probability calculations?

Answer 7

Accurate calculation and verification

Question 8

Why is understanding the properties of PDF and CDF essential?

Answer 8

For probability analysis

Question 9

How does the proper use of Z-scores enhance probability assessments?

Answer 9

Enhances probability assessments in the context of CDF

Question 13

What do Venn Diagrams utilize to represent two events?

Answer 13

Overlapping circles

For three events, an additional circle is added overlapping with the existing two.

Question 14

What do elements outside the circles in a Venn Diagram represent?

Answer 14

Items not included in the focused events.

Question 15

What is the purpose of contingency tables?

Answer 15

Display counts instead of listing all elements.

Question 16

How do contingency tables simplify representation?

Answer 16

By summarizing the sample space.

Question 17

What does P(B | A) represent?

Answer 17

Probability of event B occurring given that event A has occurred.

Question 18

What is the formula for P(B | A) if there are 6 instances of B, and 3 are favorable?

Answer 18

P(B|A) = 3/6.

Question 19

What does P(B | A Complement) signify?

Answer 19

Probability of event B given that event A has not occurred.

Question 20

What is P(A | B Complement)?

Answer 20

Probability of event A given that event B has not occurred.

Question 21

What do the probabilities of complementary events sum to?

Answer 21

1.

Question 22

What is the sum of probabilities for event A and its complement?

Answer 22

P(A) + P(A Complement) = 1.

Question 23

What do Venn diagrams and contingency tables provide?

Answer 23

Summarized and visual representation of complex probability scenarios.

Question 24

Why is it crucial to ensure conditions refer to the same sample space when calculating conditional probabilities?

Answer 24

To ensure consistency.

Question 25

What should students work on as part of their assignments?

Answer 25

The contingency tables provided.

Question 26

What should students bring to the next class?

Answer 26

Any questions or challenges encountered while working on the assignments.

Question 27

Fill in the blank: P(B) + P(B Complement) = _______.

Answer 27

1.

Question 28

True or False: Venn diagrams can be used for more than two events.

Answer 28

True.

Question 29

What is an outcome in probability?

Answer 29

Any of the possible results of an experiment ## Footnote For example, outcomes of flipping a coin are Heads and Tails.

Question 30

What are the outcomes when flipping a coin twice?

Answer 30

HH, HT, TH, TT ## Footnote Each combination represents the results of the two flips.

Question 31

Define an event in probability.

Answer 31

A subset of the possible outcomes of an experiment ## Footnote An event can be described by listing outcomes or in words.

Question 32

What is an example of event A when flipping a coin twice?

Answer 32

A = {HH, TH} ## Footnote Event A is defined as getting heads on the second coin flip.

Question 33

What is a trial in the context of an experiment?

Answer 33

One repetition or instance of the experiment ## Footnote For example, flipping a coin 10 times constitutes a trial.

Question 34

What are the outcomes when drawing two cards from a deck without replacement?

Answer 34

Every possible pair of two distinct cards ## Footnote Order matters, so (King of Hearts, 5 of Clubs) is different from (5 of Clubs, King of Hearts).

Question 35

List three outcomes in event A where two Aces are drawn.

Answer 35

(Ace of Hearts, Ace of Clubs), (Ace of Diamonds, Ace of Hearts), (Ace of Hearts, Ace of Diamonds) ## Footnote These combinations illustrate drawing two Aces from the deck.

Question 36

Is (Ace of Hearts, Ace of Hearts) an outcome in event A?

Answer 36

No ## Footnote It's impossible to draw the same card twice when not replacing cards.

Question 37

What is an independent event?

Answer 37

Events that have no influence on each other ## Footnote The occurrence of one event does not affect the probability of the other.

Question 38

What are dependent events?

Answer 38

Events that influence the occurrence of the other ## Footnote The occurrence of one event affects the probability of the other event.

Question 39

Define mutually exclusive events.

Answer 39

Events that cannot both occur ## Footnote They have no outcomes in common and are also referred to as Disjoint events.