Probability and Statistics Exam
Questions and Answers Verified
Solutions Latest Update (2026/2027)
Question:
Venn diagram and probability
Answer:
Question:
P (A n B) = A and B = A x B
P (A u B) = A or B = A + B
Arrange vs Outcomes
Answer:
Arrange - this is how many 'WAYS' something can be arranged.
think '!' (notation)
arrangement of 6 numbers without the importance of order is, 6! = 720
Question:
Outcomes - this is the result of a trial. which can also be the sample space.
(Counting principle)
Total outcome of 2 dice = 6 x 6 = 36
Independent Events
Answer:
,when the selection of one does not affect the probability of
another section.
Question:
*to make independent, terms like 'put back', 'take out' are used
TREE diagram can be used for this
The choices of letters and digits to be put on a license plate are called
independent events because each
letter or digit chosen does not affect the choices for the others.
Many answering machines allow owners to call home and get their messages
by entering a 3-digit code.
How many codes are possible?
10 x 10 x 10 = 1000
Independent Events - Example
Answer:
Question:
At a picnic, Julio reaches into an ice-filled cooler
containing 8 regular soft drinks and 5 diet soft drinks. He removes a can,
then decides he is not really
thirsty, and puts it back(this is assumption with independent questions).
What is the probability that
Julio and the next person to reach into the cooler both randomly select a
regular soft drink?
Dependent Events
Answer:
If the outcome of an event does affect the outcome of another
event, the two events are dependent.
,Question:
Look for the subordinate conjunctions: before, after, given or also ( in this
case look like what happens
first)
TREE diagram/ Formula can be used for this
Taking a piece of candy from a jar and then taking a second piece WITHOUT
replacing the first are
dependent events because taking the first piece affects what is available to
be
taken next.
Dependent Events - Diagram
Answer:
The notation reads, 'A has occurred by itself x B has
occurred AFTER A'. For example, after a student who does Math (A) he then
selects Spanish (B).
Question:
TREE diagram/ Formula can be used for this
Both events must occur in a manner where one was selected first then the
other, thus synonymous with
NOT replacing.
P(A and B) = P(A) P(B following A).
Example of a Dependent Event
Answer:
2 blue and 3 red marbles are in a bag.
Question:
, What are the chances of getting a blue marble on the second attempt, if a
blue marble was selected
first?
Identifying conditional probability
Answer:
Tip:
1. look for conjunction
2. Identify what happens first
3. use the formula and identify the 'n' eg. PnB
Question:
Look for the subordinate conjunctions: before, after, given (in this case look
like what happens first)
No Coordinating Conjunction
1. Let G denote the event 'student is girl' and let F denote the event 'student
is French'. - the probability
that if I pick a French student, it will be a girl, that is, P(F|G)
Coordinating Conjunction
2. In my town, it's rainy (R) one third of the days. Given that it is rainy, there
will be heavy traffic (T). P (T
I R)
Notation of Conditional Probability
Answer:
P(B|A) means - the probability of Event B occurring
given that Event A has already occurred.
Question:
In most examples, this means that an item is replaced
Conditional Probability example 1
Questions and Answers Verified
Solutions Latest Update (2026/2027)
Question:
Venn diagram and probability
Answer:
Question:
P (A n B) = A and B = A x B
P (A u B) = A or B = A + B
Arrange vs Outcomes
Answer:
Arrange - this is how many 'WAYS' something can be arranged.
think '!' (notation)
arrangement of 6 numbers without the importance of order is, 6! = 720
Question:
Outcomes - this is the result of a trial. which can also be the sample space.
(Counting principle)
Total outcome of 2 dice = 6 x 6 = 36
Independent Events
Answer:
,when the selection of one does not affect the probability of
another section.
Question:
*to make independent, terms like 'put back', 'take out' are used
TREE diagram can be used for this
The choices of letters and digits to be put on a license plate are called
independent events because each
letter or digit chosen does not affect the choices for the others.
Many answering machines allow owners to call home and get their messages
by entering a 3-digit code.
How many codes are possible?
10 x 10 x 10 = 1000
Independent Events - Example
Answer:
Question:
At a picnic, Julio reaches into an ice-filled cooler
containing 8 regular soft drinks and 5 diet soft drinks. He removes a can,
then decides he is not really
thirsty, and puts it back(this is assumption with independent questions).
What is the probability that
Julio and the next person to reach into the cooler both randomly select a
regular soft drink?
Dependent Events
Answer:
If the outcome of an event does affect the outcome of another
event, the two events are dependent.
,Question:
Look for the subordinate conjunctions: before, after, given or also ( in this
case look like what happens
first)
TREE diagram/ Formula can be used for this
Taking a piece of candy from a jar and then taking a second piece WITHOUT
replacing the first are
dependent events because taking the first piece affects what is available to
be
taken next.
Dependent Events - Diagram
Answer:
The notation reads, 'A has occurred by itself x B has
occurred AFTER A'. For example, after a student who does Math (A) he then
selects Spanish (B).
Question:
TREE diagram/ Formula can be used for this
Both events must occur in a manner where one was selected first then the
other, thus synonymous with
NOT replacing.
P(A and B) = P(A) P(B following A).
Example of a Dependent Event
Answer:
2 blue and 3 red marbles are in a bag.
Question:
, What are the chances of getting a blue marble on the second attempt, if a
blue marble was selected
first?
Identifying conditional probability
Answer:
Tip:
1. look for conjunction
2. Identify what happens first
3. use the formula and identify the 'n' eg. PnB
Question:
Look for the subordinate conjunctions: before, after, given (in this case look
like what happens first)
No Coordinating Conjunction
1. Let G denote the event 'student is girl' and let F denote the event 'student
is French'. - the probability
that if I pick a French student, it will be a girl, that is, P(F|G)
Coordinating Conjunction
2. In my town, it's rainy (R) one third of the days. Given that it is rainy, there
will be heavy traffic (T). P (T
I R)
Notation of Conditional Probability
Answer:
P(B|A) means - the probability of Event B occurring
given that Event A has already occurred.
Question:
In most examples, this means that an item is replaced
Conditional Probability example 1
