eog review notes - number systems
TRANSCRIPT
EOG REVIEW NOTES Number Systems
1
Adding Fraction Steps
Adding Fractions
Steps:1) Find a common denominator.
2) Convert the fractions.
3) Add the numerators and keep the denominator.
4) Simplify.
(Equivalent Denominators)
(LCM)
Adding Fraction Examples
Examples of Adding Fractions
2 33 4
+ =
8 912 12
+ =
x 4 x 3
1712 = 5
121
3 35 4
+ =
12 1520 20
+ =
x 4 x 5
2720
= 720
6
66 6 + 1 = 7 720
Subtracting Fraction Steps
Subtracting Fractions
Steps:
1) Find a common denominator.
2) Convert the fractions.
3) Subtract the numerators and keep the denominator. Borrow if necessary.
4) Subtract the whole numbers.
5) Simplify.
(Equivalent Denominators)
(LCM)
Subtracting Fractions with Whole Numbers Example
Subtracting Fractions with Whole Numbers
Subtracting Fractions with Borrowing
5 58 12 =
15 1024 24
=x 3 x 2
524
8
88
1 58 6 =
x 3 x 4
9 5
9 3 2024 245
(Borrow)8 27 2024 245 = 3 7
24
Multiplying Fraction Steps
Multiplying Fractions
Steps:
1) Convert any mixed numbers to improper fractions.
2) Cross reduce if possible.
3) Multiply straight across.
4) Simplify. 4 23
45x =
143
45x = 5615 = 3 11
15
Dividing Fraction Steps
Dividing Fractions
1) Convert any mixed numbers to improper fractions.
2) Keep, Change, Flip (KCF)
Keep the first fraction Change the operation to multiplication, Flip the second fraction to its reciprocal.
3) Follow multiplication rules.
3 5
4 6
K C F
3 6
4 5X
4 23
45 =143
45 =
K C F143
54
x = 7012 = 5 1012 = 5
56
EOG REVIEW NOTES Number Systems
2
Simplifying Fractions
Simplifying FractionsSteps
1) Find the GCF of the numerator & denominator.
2) Divide each number by the GCF.
OR
Use the upside down cake method
1620
Example
=
16 2028 1024 5
ND
(N) (D)
4/51620 16: 1, 2, 4, 8, 16
20: 1, 2, 4, 5, 10, 20
Factors44
45=
Equivalent Fractions
Equivalent FractionsSteps
Multiply or divide the numerator and denominator by the same number to get an equivalent fraction.
34 = 20
?
x 5
Example
34 = 20
?
x 5
x 5(15)
34 = 20
15
34 = 20
?
14x
Equivalent22
= 28
14x 33
= 312
37x 22
= 614
37x 33
= 921
Converting Mixed Numbers to Improper Fractions
Converting Mixed Numbers to Improper Fractions
4 35
x
+
5
(20)23
Steps
1) Multiply the denominator and the whole number.
2) Use that answer and add it to the numerator.
3) Keep your original denominator.
=
6 23
x
+
3
(18)20=
Examples
Converting Improper Fractions to Mixed Numbers
Converting Improper Fractions to Mixed Numbers
Steps
1) Divide the numerator by the denominator.
(That's your whole number)
2) The remainder is your numerator.
3) Keep your original denominator.
4) Simplify final answer.
Examples1248 =
8 1241
844
5
404
r 4
15 48 =15 12
Converting Fractions to Decimals
Converting Fractions to Decimals
Steps:
1) Divide the numerator by the denominator.
Examples:
14 4 1.00
0.25
010820200
35
5 3.00.6
030300
38
8 3.0000.375
03024605640400
Converting Decimals to Fractions
Converting Decimals to Fractions
Steps:
1) Read the number properly.
2) Write exactly how it sounds.
3) Simplify
Examples:
0.4 0.35 0.125 2.5
410 =
25
35100=
720
1251000=
18
510 =
2 122
EOG REVIEW NOTES Number Systems
3
Adding Decimals
Adding Decimals
1. Line up your decimal points.
2. Add in 0's as placeholders
2.Add each number.
3.Drop your decimal point straight down.
Examples:
4.67 + 3.9 = 0.68 + 35.7 = 15 + 8.9
4.67 00.68 15.0+ 3.908.57
1
+ 35.701
36.38+ 08.923.9
1
Subtracting Decimals
Subtracting Decimals
1. Line up your decimal points.
2. Add in 0's as placeholders
2. Subtract each number.
3.Drop your decimal point straight down.
Examples:
4.67 ‐ 3.9 = 40.68 ‐ 35.7 = 15 ‐ 8.9
4.67 40.68 15.0‐ 3.900.77
‐ 35.7004.98
‐ 08.906.1
163 3 109
16 4 10014
Multiplying Decimals
Multiplying Decimals
1. Line up your numbers.
2. Multiply without looking at the decimal points.
3.Count how many digits are to the right of each decimal point.
4.Move you decimal to the left that many times.
Example: 3.75 x 2.8 = 3.72.8x0
4
000
61
3057
1
+00501
(2) Digits to rightof decimal(1)
(3) Total
10.5
5
Dividing Decimals Example Problem
Dividing Decimals
1. Format your numbers.
2. Move decimal point in the divisor and dividend to the right until the divisor
3.Divide the numbers.
Example: 20.24 4.6 =
1 4.6 20.24
2 46. 202.4
3
004.4
1841841840
4 4.4Answer: 4.4
is a whole number.
Adding and Subtracting Integers
Adding IntegersSame Signs
1. Add the numbers
2. Use the Same Sign
Different Signs
1.Subtract the smaller # from the larger #
2.Use the sign of the larger number
Subtracting Integers
1.Copy the 1st number
2.Change the subtraction sign to addition
3.Change the 2nd numbers sign to its opposite
4.Follow the rules for adding.
(Copy‐Change‐Change)
Multiplying & Dividing
Multiplying & Dividing
1. Multiply or Divide the number without
looking at the signs.
2. If there is an Even number of negatives
your answer is Positive.
If there is an Odd number of negatives
your answer is Negative.
EOG REVIEW NOTES Number Systems
4
Opposites and Absolute Value
Absolute Value the distance from zero.
I I4 = 4 4 units
I I7 = 7 7 units
Opposites Two numbers that are equal distance from zero on the number line.Opposite of 3 is 3
3 units3 units
10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10
Multiplicative Inverse Property & Reflexive Property
Multiplicative Inverse Property
Any number multiplied by its reciprocal is always one.
a = = 1 aa
1a
= = 1 1212
43
34Example:
Reflexive Property a = a The = sign reflects the same value on both sides of the equation.
3 = 312x = 12x
15 = 2x +7 = 2x + 7 = 15Examples:
Distributive Property
Distributive Property
a(b + c) = ab + ac
Distribute what is outside of the parenthesis by what is inside the parenthesis.
Examples: 3(x + 4) =
3(x) + 3(4) =
3x + 12
Additive Inverse Property
Additive Inverse Property
a + a = 0
The sum of a number and its opposite is always zero.
Examples: 7 + 7 = 0
5 + 5 = 0
Associative Property
Associative Property
(a + b) + c = a + (b + c)
(a x b) x c = a x (b x c)
No matter how the numbers are grouped, the answer will always be the same.
Examples: (3 + 4) + 5 = 3 + (4 + 5)
(3 x 4) x 5 = 3 x (4 x 5)
Commutative Property
Commutative Property
a + b = b + a
a x b = b x a
Numbers may be added or multiplied together in any order.
Examples: 5 + 6 = 6 + 5
5 x 6 = 6 x 5
EOG REVIEW NOTES Expression and Equations
1
Distributive Property
Distributive Property Notes
Different Methods = Same Results
Box Method Arrow Method
4( x + 3) 4( x + 3)
4x 3
Multiply sides
Drop
#'s & Operation
4x 12
4x + 12
Multiply 4(x) + 4(3)
4x + 12
Remember:X + X = 2x X X = X2 , X X X = X3
Combining Like Terms
"Like" terms:• all have the same variable, same power: 3x, x, 12x
• all are constants (numbers): 14, 2.5, 1½, 5
• all have the same variable, same power: 2y2, 6y2, y2
Combining like terms: used to simplify an expression or an equation.
• circle or box the like terms in each expression or equation
• use the number in front of the variable (coefficient) and it’s sign to combine the term
Combining Like Terms Example Problem
4x2 + 6x + 9 + 3x 5
• Circle, box, or underline the like terms in each
expression or equation. Group the operation with the term.
• Use the number in front of the variable (coefficient) and
it’s sign to combine the term.
4x2 + 9x + 4
6x + 3x = 9x
+9 5 = 4
Steps:
MultiStep Equations
MultiStep Equations Example
Example Problem Completed
4(x 3) + 6x = 16 + 3x
4x 12 + 6x = 16 + 3x1) Distribute
10x 12 = 16 + 3x 4x 12 + 6x = 16 + 3x2) Combine
Like Terms
10x 12 = 16 + 3x3) Variable tosame side 3x3x
7x 12 = 164) Combine
constant terms7x 12 = 16
+12 +127x = 28
5) Solve & Check 7x = 287 7x = 4
Graphing Inequalities
x is less than or equal to 2x ≤ 2 2 ≥ x
x is less than 2x < 2 2 > x
x is greater than or equal to 2x ≥ 2 2 ≤ x
x is greater than 2x > 2 2 < x
InequalitiesGraph the Variable≥ ≤ > <
10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10
> Greater Than or equal to > Greater Than < Less Than or equal to < Less than
10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10
EOG REVIEW NOTES Expression and Equations
2
Inequalities Helpful Hints
< I I I >1 2 3
* Special Rule *If your variable term is negative you flip your inequality sign.
*Helpful Hints*If your variable is on the left side then your inequality symbol matches the arrow point.
Arrow represents values of the variable.
3 3x < 5
3x > 153x < 15
x > 2 x < 2
< I I I >1 2 3
Translating Words to Equations
Inequality Chart Words to Math Example
Writing word statements as inequalities.Steps:
1) Label the parts of the sentence.
2) Write the inequality.
Example:
+ x <7 15
x + 7 < 15
The sum of a number and 7 is less than 15
Put the operation
where the "and" is.
x + 7 < 157 7x < 8
< I I I >7 8 9
EOG REVIEW NOTES Ratios and Proportions
1
Simple Interest Formula
Simple Interest: I = Prt I = Interest paid (in dollars)P = Principal (the amount of money borrowed)r = rate (change the percent to a decimal)t = time (in years)
Interest: an amount that is collected or paid for the use of money
Simple Interest: Money paid on principal
Principal: the amount of money deposited or borrowed
Rate of Interest: percent charged or earned for the principal
Ratios
What is a Ratio?A ratio is a comparison of two quantities with the same units.
The 3 ways to write a ratio.
Remember that a ratio must always be in simplest form but have two numbers.
Colon Fraction Bar Words
2:3 23
2 to 3
Types of Ratios
Types of Ratios.There are three different types of a ratio.1) Part to Part
2) Part to Whole
3) Whole to Part
White 4 2Black 6 3
= , 2:3, 2 to 3
White 4 2Black 6 3= , 3:2, 3 to 2
White 4 2Total 10 5
= , 2:5, 2 to 5
Black 6 3= , 3:5, 3 to 5Total 10 5
White 4 2Total 10 5= , 5:2, 5 to 2
Black 6 3= , 5:3, 5 to 3Total 10 5
Unit Rates
3 1 8 96 3
1 80 990
Hours is on bottom because it says per hour.
Unit Rate is how many units of the first quantity (numerator) corresponds to one unit of the second quantity (denominator).Examples: $/lb, mi/hr, ft/sec, $/oz, mi/galJayda takes 3 hours to deliver 189
newspapers on her paper route. What is the rate per hour at which she delivers thenewspaper?
NewspapersHours
1893
= 631
Answer: 63NewspapersHour
*Hint
Unit Rate Example
If 3 cookies cost $1.59, the how much does it cost per cookie?
Words Ratio Divide Write Final Answer Cost 1.59 Cookies 3 3 1.59
0.53
150990
$0.53 per cookie
* Remeber the the word "per" shows you what is being compared (Cost per Cookie).
How to determine if each pair of ratios forms a proportion.
How to determine if each pair of ratios forms a proportion.
Examples:
43__ __8
6=
43__ __8
6=
24 = 24
4 x 6 =
8 x 3 =
Yes
46__ __3
5=
46__ __3
5=
18 = 20
4 x 5 =
3 x 6 =
No
23__ __
9=
23__ __6
9=
18 = 18
2 x 9 =
6 x 3 =
Yes
6 53__ __
4=
53__ __7
4=
21 = 20
5 x 4 =
7 x 3 =
No
7
EOG REVIEW NOTES Ratios and Proportions
2
How to set up and solve proportion word problems.
How to set up and solve proportion word problems.
Example:
4 cookies cost $6. If you have $15, how many cookies can you buy?
Word Statement(What are you comparing)
CostCookies
Proportion
64
15x
=
Top numbers represent cost and bottom numbers represent cookies.
64
15x
=
60 = 6x66
10 = x10 Cookies
How to solve a proportion with a missing value.
How to solve a proportion with a missing value.
Examples:__ __8 n=3 6
__ __8 n=3 6
3n = 483 3n = 16
Cross Multiply
Solve OneStep Equation
n = 16
__ __5 r=8 6
__ __5 r=8 6
8r = 308 8r = 3.75
r = 3.75
8 30.003.75
24605640400
Part to Whole
Percent Word Problems Part to Whole
Example:
Paul makes a gross salary of $460 each week. If 18% of his salary is withheld for taxes and social security, how much is withheld from his weekly check? How much would be withheld in a month?
Weekly: _______ Monthly: _______
% Part
100 Whole=
=10018
460x
Tax
Tax: *amount of money added to the total cost of a bill
* % = tax
Example:Your cell phone needs a new battery that will cost $10.00 plus tax. If the sales tax is 7%, how much will your total be?
100 cost
Tip
Tip: *amount of money added to the cost of a service
*calculated before tax
* % = tip 100 cost
Tip Example:
You and your friend went to lunch. The bill was $35.00. If you left the server a 15% tip, then how much tip did you leave?
Discount
Discount: *amount of money subtracted from an item or a total
* % = discount
100 cost
Discount Example:Your favorite store is having a sale. The item you buy was originally $30.00, and it is 40% off. How much is the item?
EOG REVIEW NOTES Ratios and Proportions
3
Mark Up
An increase in the cost of an item:Mark Up
To make a profit, stores have to charge more for an item than what they paid for it (wholesale amount)
Formula: % Mark Up
100 Wholesale=
Wholesale + MarkUp = Retail Price
Mark Up
Examples: Find the mark up and retail price of the following items.
Wholesale cost of a pen: $0.95
Markup: 60%
Wholesale cost of a computer: $1,850.00
Markup: 75%
Commission
CommissionThe amount of money that an individual receives based on the level of sales he or she has obtained. The sales person is provided a certain amount of money in addition to his/her standard salary based on the amount of sales obtained.
Formula:
% Commission
100 Whole=
Commission
While working at his Uncle's Car Dealership, Dontae sold this $28,194 2012 Mustang and earned a 3% commission.
Percent Change
Percent Change
Percent of change is the amount, stated as a percent, that a number increases or decreases.
Percent Change = Amount of Change
Percent Change = Largest # Smallest #
Percent Change = Difference
Original Amount x 100
Original Amount x 100
Starting AmountI I x 100
Percent Change
Percent Change Steps
1. Subtract to find the difference
2. Divide difference by original number
amount of change
original amount
3. Multiply answer by 100
% of change = amount of changeoriginal amount X 100
EOG REVIEW NOTES Geometry
1
Map Scale Proportion
To solve for missing measurements in a scale drawing you must set up a proportion. Steps:1) Write your word statement.
2) Set Up the proportion
3) Cross multiply
4) Solve the onestep equation.
5) Look at the word statement for your units.
Example: The scale of a drawing is 1/2in = 3ft
Find the measurement for 8 inches.
ftin__ __ __=
1/23
8x
24 = 1/2x__ __1/2 1/2
48 = x
Parts of a Circle
Line segment whose endpoints are the center of a circle and any point on the circle.
Radius
Diameter
Line segment that passes
through the center of a
Chord
Line segment whose endpoints
are any two points on a
circle.
circle and whose endpoints
lie on the circle.
Arc
Part of a circle named
by its endpoints
Area = Radius
Diameter
Circumference
Area and circumference
Area and Circumference of Circles
Use these to help you remember
Circumference Area
Cherry Pie's Delicious Apple Pies are too
Working Area and Circumference Backwards
Working Area and Circumference Backwards
Steps:
1) Write the formula
2) Plug in the information
3) Solve for the variable
4) Answer the question asked
Area of Shaded Regions
Finding the Area of the Shaded Region
Steps:
1) Find the total area of the figure
2) Find the area of the nonshaded figures
3) Find the difference between the areas
4) Answer the question asked
Volume of Prisms
Volume of Prisms
Volume is the amount of three dimensional space an object occupies.
V = B hB = Base Areah = height of prism
*Remember the base names the figure.Rectangular
PrismTriangularPrism
EOG REVIEW NOTES Geometry
2
Working Backwards Steps
Working Backwards with Volume Steps:
1) Read the problem.
2) Write the Formula for the answer given in the problem .
3) Substitute the information given in the problem.
4) Solve for the missing variable.
5) Make sure you have answered what the problem is asking.
Surface Area Foldable
Surface Area
Surface Area is the sum of all the areas of all the shapes that cover the surface of the object.
Steps:1) Label all sides.2) Calculate area of each shape. (Write formula, plug in numbers, then solve)3) Add all areas together.
Triangles Foldable Types of Triangles
Foldable Sum of the Interior Angles of a Triangle
Sum of the Interior Angles of a Triangle
A
B Cm A + m B + m C = 180O< < <
oThe sum of the interior angles of a triangle is always 180.
Example: Find the missing value.
112o
31o
x
31 + 112 + x = 180143 + x = 180143 143
x = 37o
EOG REVIEW NOTES Geometry
3
Relationship of Exterior Angles with Triangles
o
x
y zw
Relationship of Exterior Angles with Triangles
The sum of the exterior angle and the interior angle is equal to 180 because they make a straight line.
m w + m y = 180O< <
Relationship of Exterior Angles with Triangles
x
y zw
Relationship of Exterior Angles with Triangles
The exterior angle must be equal to the sum of the remote interior angles.
m w = m x + m z< < <
Quick Review
Acute Angle Right Angle Obtuse Angle
Less than 90
Parts of an Angle Naming Angles
o Exactly 90o Greater than 90
Vertex Side: Ray
Side: Ray
Interior: Inside of angle
Exterior: Outside of angle
CommonEndpoint( )
A
B C<ABC or CBA<
* Vertex must always be in the middle
o
Types of Angles
Types of Angles
Complementary Two Angles are Complementary when they add up to 90 degrees (a Right Angle).
Supplementary Two Angles are Supplementary when they add up to 180 degrees.
Vertical Vertical Angles are the angles opposite each other when two lines cross. They are always equal.
Adjacent Two angles are Adjacent when they have a common side and a common vertex (corner point), and don't overlap.
Complementary Angles
Complementary Two Angles are Complementary when they add up to 90 degrees (a
Right Angle).
B<A<
m A + m B = 90< < o
Challenge Question:
If m A equals 43, Find m B.< <o
If m A equals 2x + 4 and m B equals 3x 14, solve for x.
< <
m A + m B = 90< <o
(2x + 4) + (3x 14) = 90
2x + 4 + 3x 14 = 90
5x 10 = 90
5x 10 = 90+ 10 +105x = 1005 5
m A + B = 90< <o
(43)+ B = 9043 43
B = 47 o
ox = 20
Supplementary Angles
Supplementary Two Angles are Supplementary when they add up to 180 degrees.
BAm A + m B = 180< <
o
Challenge Question:
If m A equals 83, Find m B.< <o
If m A equals 3x + 36 and m B equals 7x +14, solve for x.
< <
m A + m B = 180< < o
(3x + 36) + (7x + 14) = 180
3x + 36 + 7x + 14 = 180
10x + 50 = 180
10x + 50 = 180 50 5010x = 13010 10x = 13
m A + m B = 180< <o
(83)+ m B = 18083 83
B = 97 o
o
<
EOG REVIEW NOTES Geometry
4
Vertical Angles
Vertical Vertical Angles are the angles opposite each other when two lines cross. They are always equal.
B
A
m A = m B < <Challenge Question:
<
If m A equals 6x + 9 and m B equals 81, solve for
<<
m A = m B <
<(6x + 9) = (81 )
C D
m C = m D < <&
o
6x + 9 = 81 9 96x = 726 6x = 12
If m A equals 113, Find m B.<o
m A = m B < <(113) = m B <
o x.
Adjacent Angles
Adjacent Two angles are Adjacent when they have a common side and a common vertex (corner point), and don't overlap.
B<A<
A< B<
B<A<
Common Side
Common Vertex
A< B<C<D<
A is adjacent to ___ & ___ <B is adjacent to ___ & ___
C is adjacent to ___ & ___
D is adjacent to ___ & ___
<
<
<
<
<
<
<
<
<
<
<
D B
A C
D B
A C
EOG REVIEW NOTES Statistics and Probability
1
Mean
Mean
The _____________ of the numbers in a set of data _____________ by the total number of pieces of data.
Average or Equal Share
Example: 18, 19, 21, 22
Mean = ___________
sumdivided
Sum = 18 + 19 + 21 + 22 = 80Divide by 4 = 80/4 = 20
20
Median
Median
The number in the _____________ of a set of data when the data are arranged in order.
If there are two numbers the
median is their average.
Example: 10, 11, 13, 15, 19
Example #1 Median = ___________
middle
* Mark out the ends as pairs13
Example #2: 10, 11, 13, 14, 15, 19 Find the average: (13+14)/2 = 13.5
Example #2 Median = ___________13.5
Mode
Mode
The number that occurs __________ often.
Example: 75, 78, 80, 80, 90, 100, 101
Mode = ___________
most
80
Range
Range
_____________ between the maximum and the minimum.
Example: 18, 19, 21, 22
Range = ___________
Difference
22 18 = 4
4
Outlier
Outlier
A number in a data set that is ____________ smaller or larger than the other numbers.
Example: 55, 80, 75, 90, 85, 95, 100, 100
Outlier = ___________
significantly
55
Variation
Variation
A measure of how ______________ a set of data is.
Example: 75, 78, 80, 80, 90, 100, 101
There is a cluster around _____________.
A gap is from _____________.
The range is _____________.
spread out
75 80
80 90
26
EOG REVIEW NOTES Statistics and Probability
2
Completed Box and Whisker Plot
2, 3, 5, 6, 8, 9, 12, 12, 13Median
of entire setLeast Value
GreatestValue
Median of lower half Median of upper half
4 12
Lower Quartile Upper Quartile
2 4 6 8 10 12 14*If the median falls between two numbers you have to average them. (Add and divide by 2)
Completed Box and Whisker Plot
2, 3, 5, 6, 8, 9, 9, 12, 12, 13
Medianof entire set
Least Value
GreatestValue
Median of lower half Median of upper half
5 12Lower Quartile Upper Quartile
2 4 6 8 10 12 14
8.5
*If the median falls between two numbers you have to average them. (Add and divide by 2)
Identifying Information on a Box and Whisker Plot
Lower Extreme The ______ number in the data set.
1st Quartlie The middle number of the _________ half of the data.
2nd Quartile The middle number of the data set. Also know as the _________.
3rd Quartile The middle number of the _________ half of the data.
Upper Extreme The _______ number in the data set.
Interquartile Range (IQR) The range of the ______
(between the _____ and the ____ quartiles.)
smallest
1st/lower
median
2nd/upper
largest
box
1st 3rd
MAD Notes
Mean Absolute Deviation
The mean absolute deviation or MAD of a set of data is the average distance between each data value and the mean.
Steps to find the MAD:
1. Find the mean of the data.
2. Find the distance (absolute value) between each data value and the mean.
3. Add the distances together and divide by the number of data points. This answer is the MAD.
Experimental Probability
Experimental Probability
Favorable Outcome
What does happen?
Example: You toss a die 10 times. You record the number. You want to find the experimental probability of getting a 3.
If 3 occurred 6 times, the probability is
Number of Trials Conducted
610 = 3
5
Theoretical Probability
Theoretical Probability
Favorable Outcome
What should happen?
Example: There are 6 numbers on a die. You want to find the theoretical probability of getting a 3.
The probability of rolling a 3 =
When tossing a die you should get a 3 one sixth of the time.
Total Possible Outcomes
16
EOG REVIEW NOTES Statistics and Probability
3
Outcomes
Determining OutcomesSteps:
1) Divide the items into groups.
2) Determine how many items are in each group.
3) Multiply.
Fundamental Counting Principle (FCP)
If an event has m possible outcomes and another independent event has n possible outcomes, then there are mn possible outcomes for the two events together
Outcomes
OutcomesA restaurant offers dinner specials consisting of a main course, one vegetable and one dessert.If there are 2 main courses, 3 vegetables, and 2 desserts, how many dinner specials are possible?
FCP = 2 3 2
12 outcomesM1
V1
V2
V3
D1 M1V1D1D2 M1V1D2D1 M1V2D1D2 M1V2D2D1 M1V3D1D2 M1V3D2
M2
V1
V2
V3
D1 M2V1D1D2 M2V1D2D1 M2V2D1D2 M2V2D2D1 M2V3D1D2 M2V3D2
Simple and Compound Events
Simple Compound