Download MDM 4U Unit 3: Probability Review and Preview of Probability

MDM 4U
Unit 3: Probability
Review and Preview of Probability Assignment
Due Wednesday, October 3, 3012
Name: ______________________
The following assignment is to be started in class following the Unit 2 test and completed for
homework. Assignments are to be your own work! Any assignments handed in which are the
same form, set up, errors, etc. (I.e. simply copied from someone else) will not be evaluated.
1.
Review of Prerequisite Skills:
Probability involves being able to count the number of ways an event can occur or the total number
of possible outcomes to an experiment. To prepare for this unit you will review some counting
theory.
Complete the following showing full and justified solutions.
Page 302 # 6, 7, 8, 9, 10, 13, 14, 16, 17
2.
**Check your answers in back of text!
Explain the meaning of each of the following terms and give an example.
Read pages 304 – 307 and use the Glossary at the back of the text to help.
a) Probability
b) Probability Experiment
c) Trials
d) Outcomes
e) Sample Space, S
f) Events
g) Probability of an Event and what value it can have.
h) Empirical Probability
i) Theoretical Probability and how to calculate it.
Review and Preview of Probability Assignment
Due Wednesday, October 3, 3012
MDM 4U
Category
Knowledge/
Understanding
Communication
Application
Name: ______________________
Level 4
Level 3
Level 2
Level 1
Below Level 1
Demonstrates a solid and
thorough understanding
of counting principles and
probability terminology.
Demonstrates good
understanding of
counting principles and
probability
terminology.
Demonstrates moderate
understanding of
counting principles and
probability terminology
Demonstrates a limited
or inaccurate
understanding of
counting principles and
probability terminology
Demonstrates
insufficient
understanding of
counting principles and
probability terminology
Provides a thorough,
clear and insightful
explanation/justification
(solutions are well
formed, with
completeness, accuracy
and full proper
mathematical form)
Provides a complete,
clear, and logical
explanation, missing
small details (solutions
are complete but some
proper form is missing
–i.e. therefore
statements)
Provides a partial
explanation/justification
that shows some clarity
and logical thought
(solutions are somewhat
complete, but
disorganized)
Provides a limited or
inaccurate
explanation/justification
that lacks clarity or logical
thought (solutions are
incomplete, scattered and
disorganized)
Demonstrates insufficient
understanding of proper
mathematics form for
solutions (solutions are
minimal and incomplete,
no math form show)
Assignment is complete,
handed in on time and
completely demonstrates
the individual student’s
thinking.
Assignment is
complete, handed in
on time and most work
demonstrates the
individual student’s
thinking.
Assignment is complete,
handed in on the due
date and some of the
work demonstrates the
individual student’s
thinking while some
shows input from others.
Assignment is almost
complete, handed in on
the due date and
demonstrates little of the
individual student’s
thinking while most shows
input from others.
Assignment has little work
complete and/or was not
handed in on the due date
and/or is a copy of
someone else’s work.
Confidently and
accurately applies
probability and counting
concepts to solve
problems with no error.
Confidently applies
probability and
counting concepts to
solve problems with
little error.
Somewhat applies
probability and counting
concepts to answer
questions.
Applies limited probability
and counting concepts to
answer questions.
Insufficient probability and
counting concepts applied
to answer questions.
Review and Preview of Probability Assignment
Due Wednesday, October 3, 3012
Solutions
1.
Review of Prerequisite Skills:
Probability involves being able to count the number of ways an event can occur or the total
number of possible outcomes to an experiment. To prepare or this unit you will review
some counting theory.
Complete the following showing full and justified solutions.
Page 302 # 6, 7, 8, 9, 10, 13, 14, 16, 17
**Check your answers in back of text!
2.
Explain the meaning of each of the following terms and give an example.
Read pages 304 – 307 and use the Glossary at the back of the text to help.
a) Probability: is the branch of mathematics that deals with chance, random
variables, and the likelihood of outcomes.
Ex. The probability of rain is 60% today.
b) Probability Experiment: a well defined process consisting of a number
of trials in which clearly distinguishable outcomes are observed.
Ex. Flip a coin 10 times and record whether you flip heads or tails.
c) Trials: A step in a probability experiment in which an outcome is
produced and tallied.
Ex. From b) each flip of the coin is a trial.
d) Outcomes: possible results of an experiment or action.
Ex. The outcome of the coin flipping experiment would be how many
head or tails and in what order they happened. HHHTTHTTTH is one
possible outcome.
e) Sample Space, S: The set of all possible outcomes in a probability
experiment.
Ex.
The sample space for the coin flipping experiment would be the set
of all the different ways the 10 trials could have turned out.
f) Event: A group of outcomes to an experiment with specified
characteristics.
Ex. Event A could be the set of outcomes where there were 3 Heads and 7
Tails.
g) Probability of an Event and what value it can have: P(A), is a quantified
measure of the likelihood that the event will occur. The probability of an event is always
a value between 0 and 1.
Ex. When you flip a coin the probability of getting Tails is 0.5
h) Empirical Probability: (also called experimental or relative frequency probability)
is determined by dividing the number of times that the event actually occurs in an
experiment by the number of trials.
Ex. If you found that 3 of the ten trials had 3 Heads and 7 Tails, then the Emperical
3
Probability of getting 3 heads in 10 flips if 10 .
i) Theoretical Probability and how to calculate it: is deduced from
analysis of the possible outcomes.
For example if all outcomes are equally likely then
P(A) = n(A)
n(S)