Probability and Statistics C459 Exam
Questions and Answers Verified
Solutions Latest Update (2026/2027)
Question:
Basic Probability Rules
Answer:
Rule 1
For any event A, 0 ≤ P(A) ≤ 1.
This first rule simply reminds us of the basic property of probability that
we've already learned. The
probability of an event, which informs us of the likelihood of it occurring, can
range anywhere from 0
(indicating that the event will never occur) to 1 (indicating that the event is
certain).
Question:
Rule 2
P(S) = 1; that is, the sum of the probabilities of all possible outcomes is 1.
Rule 3: The Complement Rule
P(not A) = 1 - P(A); that is, the probability that an event does not occur is 1
minus the probability that it
does occur.
Rule 4: The Addition Rule for Disjoint Events
The Addition Rule for Disjoint Events: If A and B are disjoint events, then P(A
or B) = P(A) + P(B).
Rule 5: The Multiplication Rule for Independent Events
If A and B are two independent events, then P(A and B) = P(A) * P(B).
,P(A and not B)=[since independent]=P(A)*P(not B)=0.37*0.63
Rule 6: The General Addition Rule
For any two events A and B, P(A or B) = P(A) + P(B) - P(A and B).
what statistics is all about is
Answer:
converting data into useful information. Statistics is
therefore a process where we are:
collecting data,
summarizing data, and
interpreting data.
Question:
The process of statistics starts when we identify what group we want to
study or learn something about.
We call this group
Answer:
The population
Question:
In statistics population
Answer:
Question:
can refer not only to people, but also to animals, things etc
Population
,Answer:
Question:
is the entire group that is the target of our interest:
Sample
Answer:
A more practical approach would be to examine and collect data only from a
sub-group of the population. Use this approach when the population is too
large to conduct to collect
data from.
Question:
We call this first step, which involves choosing a sample and collecting data
from it
Answer:
Question:
Producing data
choose a sample in such a way
Answer:
Question:
that it will represent the population well
Exploratory Data Analysis
, Answer:
Summarizing the collected data
Question:
Probability
Answer:
the "machinery" that allows us to draw conclusions about the population
based on the data collected about the sample.
Question:
Inference
Answer:
Finally, we can use what we've discovered about our sample to draw
conclusions about our population.
Question:
The Big Picture," the four-step process that encompasses statistics
Answer:
1. Producing Data-
Choosing a sample from the population of interest and collecting data.
Question:
Questions and Answers Verified
Solutions Latest Update (2026/2027)
Question:
Basic Probability Rules
Answer:
Rule 1
For any event A, 0 ≤ P(A) ≤ 1.
This first rule simply reminds us of the basic property of probability that
we've already learned. The
probability of an event, which informs us of the likelihood of it occurring, can
range anywhere from 0
(indicating that the event will never occur) to 1 (indicating that the event is
certain).
Question:
Rule 2
P(S) = 1; that is, the sum of the probabilities of all possible outcomes is 1.
Rule 3: The Complement Rule
P(not A) = 1 - P(A); that is, the probability that an event does not occur is 1
minus the probability that it
does occur.
Rule 4: The Addition Rule for Disjoint Events
The Addition Rule for Disjoint Events: If A and B are disjoint events, then P(A
or B) = P(A) + P(B).
Rule 5: The Multiplication Rule for Independent Events
If A and B are two independent events, then P(A and B) = P(A) * P(B).
,P(A and not B)=[since independent]=P(A)*P(not B)=0.37*0.63
Rule 6: The General Addition Rule
For any two events A and B, P(A or B) = P(A) + P(B) - P(A and B).
what statistics is all about is
Answer:
converting data into useful information. Statistics is
therefore a process where we are:
collecting data,
summarizing data, and
interpreting data.
Question:
The process of statistics starts when we identify what group we want to
study or learn something about.
We call this group
Answer:
The population
Question:
In statistics population
Answer:
Question:
can refer not only to people, but also to animals, things etc
Population
,Answer:
Question:
is the entire group that is the target of our interest:
Sample
Answer:
A more practical approach would be to examine and collect data only from a
sub-group of the population. Use this approach when the population is too
large to conduct to collect
data from.
Question:
We call this first step, which involves choosing a sample and collecting data
from it
Answer:
Question:
Producing data
choose a sample in such a way
Answer:
Question:
that it will represent the population well
Exploratory Data Analysis
, Answer:
Summarizing the collected data
Question:
Probability
Answer:
the "machinery" that allows us to draw conclusions about the population
based on the data collected about the sample.
Question:
Inference
Answer:
Finally, we can use what we've discovered about our sample to draw
conclusions about our population.
Question:
The Big Picture," the four-step process that encompasses statistics
Answer:
1. Producing Data-
Choosing a sample from the population of interest and collecting data.
Question:
