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Algebra 1
Name: _________________________________
Date: _______________
GRADE:
/40 pts
PROBABILITY
Probability is a branch of mathematics that deals with the possibility, or likelihood, that an
event will happen.
This is an independent study of probability that you will work on in class and at home. Upon
completion, this packet will provide notes, examples, and practice on the topic of probability.
Unless noted, each section is worth 5 points largely based on effort and completeness.
Part I. Introduction
Read “Intuitive Idea of Probability” at
http://www.regentsprep.org/Regents/math/probab/LProb.htm and complete the following notes.
The probability of an event occurring can be expressed as the following ratio:
probability of an event 
The probability of an event happening is between 0 and 1. If an event is impossible, the
probability is zero. If an event is certain, the probability is one. This can be expressed as a
continuum:
0
0.25
0.50
0.75
1.00
Complete the chart above based on the Regentsprep reading.
Part II. Theoretical vs. Empirical Probability
Return to RegentsPrep and read about “Theoretical vs. Empirical Probability” at
http://www.regentsprep.org/Regents/math/probab/theoProp.htm. Complete the following:
Define:

Empirical (Experimental) Probability:
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
Theoretical Probability:

Event:

Outcomes:

Sample Space:
ACTIVITY:
Read the first three paragraphs of “Heads or Tails” at
http://www.usoe.k12.ut.us/curr/science/sciber00/7th/genetics/sciber/probab.htm. With a
partner, conduct the coin toss experiment using the “coin toss” simulator at
http://nlvm.usu.edu/en/nav/frames_asid_305_g_3_t_5.html. Record your data in the chart
below.
Number of
tosses
Probability
10
50
100
1. What is the theoretical probability that when a coin is tossed, heads will come up?
2. Using the coin toss simulation, you conducted experiments to determine the empirical
(experimental) probability. What conclusion can you draw from your experiment?
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Conduct a similar experiment with a spinner at:
http://nlvm.usu.edu/en/nav/frames_asid_186_g_3_t_5.html?open=activities. Select record
results and enter 10 spins. Record the data in the chart. Then without clearing chart, do with 50
spins and 100 spins. Calculate the experimental probability based on the total number of spins
(160).
# spins
Red
Orange
Purple
Yellow
Green
10
50
100
Probability:
(total spins
= 160)
1. What is the theoretical probability of landing in the red region? The experimental
probability?
2. What could you do to make the experimental probability approximately the same?
Part III. Odds
Often confused with probability, odds is another way of measuring the chance of an event
occurring.
The odds of an event occurring is a ratio that compares the number of favorable outcomes
(successes) to the number of unfavorable outcomes (failures). Based on this definition, express
odds as a ratio:
Odds 
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Example:
A bag contains 6 red marbles, 3 blue marbles, and 1 yellow marble. Find the odds of choosing a
red marble.

The number of favorable outcomes equals the number of red marbles or 6.

The number of unfavorable outcomes equals the sum of marbles that are NOT RED or 4.

The odds of choosing a red marble are 6:4 or (simplified) 3:2.
Practice:
1. Find the odds of each outcome if a die is rolled:
a.
a number greater than 4
b.
an even number.
Part IV. Compound Events
The previous 3 sections dealt with simple events; however, there are many situations in which
probability is influenced by two or more simple events that are either dependent or independent
of each other.
Compound events can be joined by “and” or “or.” Two events connected by “or” are described as
mutually exclusive. Read about mutually exclusive events at:
http://www.regentsprep.org/Regents/math/mutual/Lmutual.htm.
From the reading:
1. Referring to the examples, explain why rolling a 7 or 11 are mutually exclusive events yet
rolling a 6 or doubles is NOT mutually exclusive.
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2. Summarize the formulas:
a. If A and B are mutually exclusive events, then
P (A or B) =
b. If A and B are NOT mutually exclusive events (also referred to as INCLUSIVE), then
P (A or B) =
HINT: One way to determine if two events are mutually exclusive or NOT is to look at the
sample space for each event separately to see if there is any overlap. If there are shared
outcomes, the events are NOT mutually exclusive!
Independent events are two events in which the outcome of one event does not affect the
outcome of the other.
Read about independent events at:
http://www.regentsprep.org/Regents/math/mutual/Lindep.htm and then complete the following
notes.
If A and B are independent events, then:
P (A and B) =__________________________
Example:
A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find the probability of
drawing a red chip, replacing it, then drawing a green chip.
Total number of chips = __________
Probability of drawing a red chip [ P(red) ] =
# red chips
total # chips
Probability of drawing a green chip [ P(green) ] =
= ______________
# green chips
total # chips
= ____________
P(red, green) = P(red)  P(green)
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Define dependent event:
If A and B are dependent events, then:
P (A and B) =__________________________
Example:
A bin contains 8 blue chips, 5 red chips, 6 green chips, and 2 yellow chips. Find the probability of
selecting two yellow chips without replacement.
Total number of chips = ___________________
Probability of selecting a yellow chip [ p(yellow) ] =
# yellow chips
total # chips
Probability of selecting a second yellow [ p(yellow) ] =
= ___________
# yellow chips  1
total # chips  1
= ________
P(yellow, yellow) = P(yellow)  P(yellow)
Note that in addition to the total number of chips being reduced by one because the first yellow
chip was not replaced, there is one less yellow chip as well.
Part V. Applying Probability to Genetics
In Biology, probability is applied to the study of genetics. A table, called a Punnett Square, is
used to determine the probability that a child will inherit certain genes from his or her parents.
Return to “Heads or Tails”
(http://www.usoe.k12.ut.us/curr/science/sciber00/7th/genetics/sciber/probab.htm) and
continue reading from “Another example…” which describes how the probability of a baby’s sex
is calculated. After reading, answer the following questions:
1. Is the sex of a baby influenced by the sex of earlier children?
2. If a family already has 5 girls, what is the probability the 6th child will be a boy?
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Now, read “Fun with Punnett Squares”
(http://www.usoe.k12.ut.us/curr/science/sciber00/7th/genetics/sciber/punnett.htm) paying
particular attention to the calculation of the probability that the offspring of a tall pea plant
and a short pea plant will be tall. Then complete the following example:
Example:
Each person carries two types of genes for eye color. The gene for brown eyes (B) is dominant
over the gene for blue eyes (b). That is, if a person has one gene for brown eyes and the other
for blue, that person will have brown eyes. The Punnett Square below shows the genes for the
two parents.
B
b
B
BB
Bb
b
Bb
bb
1. What is the probability that any child will have blue eyes?
2. What is the probability that the couple’s two children both have brown eyes?
3. Find the probability that the first or second child has blue eyes.
Part VI. Expressing Yourself (10 pts)
The final aspect of this study of probability is an opportunity to read about the connection
between probability and genetics and to comment on the issue posed in the short reading
selection.
1. Read “How Big a Pig Will I Be?” at http://www.petpigs.com/news/nanews67.htm.
2. Go to our class page on SchoolWires and select the “D-Blog” button on the sidebar menu.
3. Post two comments as follows: ONE to the question posed, and, TWO in response to a
classmate’s posting. Please keep all comments civil and appropriate.
IMPORTANT: To receive credit for this part of the assignment, write the NAME you are using
on the blog: _____________________________________
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Part VII. PROBABILITY PRACTICE SET (Show all calculations—even for multiple choice!)
1. A card is chosen at random from a deck of 52 cards. Find the probability of choosing each of
the following:
a.
P(a red card)
b.
P(the jack of diamonds)
c.
P (an ace)
d.
P(a black 10)
2. Two dice are rolled. What is the probability that the sum of the two numbers is 9?
a.
d.
1
6
1
36
c.
d.
1
9
2
3
3. This spinner is spun two times. What is the probability that the arrow will land on 3 the first
time and on the 4 the second time?
3 2
4
3
3
4
2
a.
d.
3
1
c.
2
1
4
d.
1
8
1
9
4. A jar has 2 yellow marbles, 3 red marbles, 5 green marbles, and 2 blue marbles.
A. What is the probability of picking 3 red marbles in a row if you replace your marble after
each pick?
a.
b.
1
12
1
64
c.
d.
1
4
1
9
B. What is the probability of picking a yellow marble, then a blue marble, then another yellow
marble if you DO NOT replace your marble after each pick?
a.
b.
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288
1
220
c.
d.
1
432
1
330
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