Chapter 2

Question 1

What is an experiment?

Answer 1

An experiment is a procedure that is carried out under controlled conditions, and executed to discover an unknown result

Example: Changing an ingredient in a recipe or flipping a coin

Question 2

Define a random experiment.

Answer 2

A random experiment is a procedure that is carried out under controlled conditions, and executed to discover an unknown result

Question 3

What is a sample space?

Answer 3

The set of all possible outcomes of a random experiment

Question 4

What is a discrete sample space?

Answer 4

A sample space is discrete if it consists of a finite or countable infinite set of outcomes

Question 5

What is a continuous sample space?

Answer 5

A sample space is continuous if it contains an interval (either finite or infinite) of real numbers

Question 6

In the context of camera flash recycle times, what type of sample space is represented by the positive real numbers?

Answer 6

Continuous

Question 7

In the context of camera flash recycle times, what type of sample space is represented by the values low, medium, or high?

Answer 7

Discrete

Question 8

What is an event in probability?

Answer 8

An event refers to outcomes of interest from a random experiment

Question 9

What does the union of two events consist of?

Answer 9

The union consists of all outcomes that are contained in either of the two events, denoted as A ∪ B

Question 10

What does the intersection of two events consist of?

Answer 10

The intersection consists of all outcomes that are contained in both of the two events, denoted as A ∩ B

Question 11

How is the complement of an event defined?

Answer 11

The complement of an event A in a sample space is the set of outcomes in the sample space that are not in A, denoted as A’

Question 12

What is a null set in probability?

Answer 12

The null set is the event that contains no outcomes

Question 13

What is the purpose of Venn diagrams in probability?

Answer 13

Venn diagrams are used to represent a sample space and events in a sample space

Question 14

Define mutually exclusive events.

Answer 14

Mutually exclusive events are events that cannot occur at the same time

Question 15

What are counting techniques in probability?

Answer 15

Counting techniques are methods used to determine the outcomes in the sample space or events, including multiplication rule, permutations, and combinations

Question 16

What is the Multiplication Rule in counting?

Answer 16

The total number of ways to complete a sequence of operations is the product of the number of ways to complete each individual step

Question 17

Give an example of the Multiplication Rule.

Answer 17

Designing a website with four colors, three fonts, and three image positions results in 4 x 3 x 3 = 36 different designs

Question 18

Define a permutation.

Answer 18

A permutation of the elements is an ordered sequence of the elements

Question 19

What is the formula for permutations of subsets?

Answer 19

The number of permutations of subsets of r elements selected from a set of n different elements is given by n! / (n - r)!

Question 20

Define combinations in probability.

Answer 20

In combinations, order is not important

Question 21

What is the difference between permutations and combinations?

Answer 21

Permutations consider the order of elements, while combinations do not

Question 22

What is subjective probability?

Answer 22

Subjective probability is the degree of belief, where different individuals may assign different probabilities to the same outcomes

Question 23

What does a probability value of 0 indicate?

Answer 23

An outcome will not occur

Question 24

What does a probability value of 1 indicate?

Answer 24

An outcome will occur with certainty

Question 25

What is the range of values for probability?

Answer 25

[0, 1] or from 0 to 100%.

Question 26

What does a probability of 0 indicate?

Answer 26

An outcome will not occur.

Question 27

What does a probability of 1 indicate?

Answer 27

An outcome will occur with certainty.

Question 28

Define subjective probability.

Answer 28

Degree of belief.

Question 29

What is an example of subjective probability?

Answer 29

The chance of rain today is 30%.

Question 30

Define relative frequency probability.

Answer 30

The limiting value of the proportion of times the outcome occurs in n repetitions of the random experiment.

Question 31

How can a probability assignment be interpreted in relative frequency probability?

Answer 31

If we assign probability 0.2 to an outcome, approximately 20% of occurrences will reflect this outcome.

Question 32

In a random selection of 1 laser diode from a batch of 100, what probability is assigned to each outcome?

Answer 32

0.01.

Question 33

What is the probability of an event in a discrete sample space?

Answer 33

Defined by the reasoning used in the random selection example.

Question 34

List the events defined in Example 2.13.

Answer 34

* A: {a, b} * B: {b, c, d} * C: {d}

Question 35

What are mutually exclusive events?

Answer 35

Events that cannot occur at the same time.

Question 36

Why can't we just add P(A) and P(B) in Example 2.13?

Answer 36

Because events A and B share a common outcome (b).

Question 37

What is the first axiom of probability?

Answer 37

P(S) = 1.

Question 38

What is the range of probability for any event E?

Answer 38

0 ≤ P(E) ≤ 1.

Question 39

What does it imply if E1 is contained in E2?

Answer 39

P(E1) ≤ P(E2).

Question 40

What are joint events generated by?

Answer 40

Applying basic set operations to individual events.

Question 41

List the basic set operations for joint events.

Answer 41

* Unions of events * Intersections of events * Complements of events

Question 42

In Example 2.15a, what is P(H) for the event of contamination?

Answer 42

358/940.

Question 43

In Example 2.15a, what is P(C) for the event of being in the center of a sputtering tool?

Answer 43

626/940.

Question 44

What is the event that a wafer is from the center of the sputtering tool or contains high levels of contamination called?

Answer 44

The union of events.

Question 45

What is a practical interpretation of contamination sources in semiconductor wafers?

Answer 45

Yield from different locations on wafers are routinely aggregated.

Question 46

How do you compute P(H ∩ C)?

Answer 46

Using the addition rule and relevant probabilities.

Question 47

What is the addition rule in probability?

Answer 47

A rule that provides a way to calculate the probability of the union of two events.

Question 48

Fill in the blank: The probability of an event is assigned to each member of a collection of events from a _______.

Answer 48

[random experiment].