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Properties Theoretical

Probability

+, -, *, /

Rational #’s

Experimental

ProbabilityVocabulary

Properties for $100

Name the Property shown below:

b + 0 = b

Answer

Identity Property of Addition

Back

Properties for $200

Name the Property shown below:

7 + (3 + C) = (7 + 3) + C

Answer

Associative Property of Addition

Back

Properties for $300

Name the Property shown below:

2*b = b*2

Answer

Commutative Property of Multiplication

Back

Properties for $400

Name the Property shown below:

5(1/5) = 1

Answer

Inverse Property of Multiplication

Back

Properties for $500

Simplify the expression. Justify each step.

6x + 4(3 + 9x)

Answer

6x + 4(3 + 9x)

6x + 4*3 + 4 *9x => Distributive Property

6x + 12 + 36x => Multiplication

6x + 36x + 12 => Commutative Property of addition

(6 + 36)x + 12 => Distributive Property

42x + 12 => Addition

Back

Theoretical Probability for $100

If I roll a dice one time, what is the probability of rolling a one or a three?

i.e. P(1 or 3) = ?

Answer

Number of Items in Sample Space = 6

Sample Space {1 2 3 4 5 6}

Probability = 2/6 or 1/3

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Theoretical Probability for $200

If I flip a coin 4 times, what is the probability of the same face showing up all 4 times?

i.e. Either H-H-H-H or T-T-T-T

Answer

Elements in Sample Space = 2*2*2*2 = 16

P(H-H-H-H) = 1/16

P(T-T-T-T) = 1/16

P(H-H-H-H OR T-T-T-T)

= (1/16) + (1/16) = 2/16= 1/8

Back

Theoretical Probability for $300

Suppose you choose an m&m from a bag containing 5 blue m&m’s, 4 red m&m’s and 7 yellow m&m’s. You then pick another m&m. Find P(red then yellow)

Answer

P(red then yellow)

Number of Items in Sample Space: 16

Sample Space {b b b b b r r r r y y y y y y y}

Event 1: P(red) = 4/16 = ¼

New Sample Space {b b b b b r r r y y y y y y y}

Event 2: P(yellow) = 7/15

P(red then yellow) = ¼ * 7/15 = 7/60

Back

Theoretical Probability for $400

Draw the sample space for the following event:

You flip a coin, and then spin the spinner shown below.

Answer

{Back

}H-O

H-P

H-Y

H-G

H-R

T-O

T-P

T-Y

T-G

T-R

Theoretical Probability for $500

I spin the spinner shown below, and then roll a dice. Find P(Red and 2)

Answer

Number of elements in sample space:

5 * 6 = 30

P(Red) = 1/5

P(2) = 1/6

P(Red and 2) = (1/5) * (1/6) = 1/30

Back

Experimental Probability for $100

If I draw 35 cards out of a bag, and 7 or them are hearts, what is the experimental probability of drawing a heart?

Answer

7/35 = 1/5

Back

Experimental Probability for $200

What is the experimental probability of thinking Mr. Paul is funny if out of 98 randomly chosen students, 2 thought he was funny?

Answer

2/98 = 1/49 = 2.04%

Back

Experimental Probability for $300

I rolled a dice 12 times, and the results are shown below. What is the experimental probability of rolling a 6?

3, 5, 1, 5, 4, 6, 6, 3, 6, 3, 5, 3

Answer

Items in Sample Space: 12

Sample Space:

{3, 5, 1, 5, 4, 6, 6, 3, 6, 3, 5, 3}

Favorable outcomes in sample space: 3

Experimental Probability= 3/12 = ¼ = 25%

Back

Experimental Probability for $400

If I randomly pick 24 of the 66 eighth graders at AIS and find that 8 of them are eating pizza for lunch, how many of the 66 total eighth graders would we expect to be eating pizza?

Answer

Experimental Probability = 8/24 = 1/3

Total 8th graders = 66

Total Students Eating Pizza Expected

= (1/3) * 66 = 22 Students

Back

Experimental Probability for $500

There are 452 dogs that live in district 1. If I randomly select 69 of the dogs, and find that 29 are small dogs, what is the experimental probability of a dog being small AND how many of the 452 dogs in district 1 would we expect to be small dogs?

Answer

Experimental Probability = 29/69

Total Dogs in District 1 = 452

Total Small Dogs Expected

= (29/69) * 452 = 190 Dogs

Back

Vocabulary for $100

Define the following word:

Coefficient

Answer

Coefficient – The numerical factor of a term (a number, a variable, or the product of a number and one or more variables)

Back

Vocabulary for $200

Define the following word:

Matrix

Answer

Matrix – a rectangular arrangement of numbers in rows and columns

Back

Vocabulary for $300

Define the following word:

Like Terms

Answer

Like Terms – Terms (a number, a variable, or the product of a number and one or more variables) that have exactly the same variable factors

Back

Vocabulary for $400

Define the following word:

Sample Space

Answer

Sample Space – The set of all possible outcomes of an event

Back

Vocabulary for $500

Define the following word:

Complement of an Event

Answer

Complement of an Event – All of the possible outcomes not in the event.

i.e. all of the items in the sample space that do not satisfy the given event

Back

Operations on of Rational #’s for $100

Solve:

5 - -3 + 9*3

Answer

5 - -3 + 9*3

= 5 - -3 + 27

= 8+27

= 35

Back

Operations on of Rational #’s for $200

Solve:

-3 *|3-5|

-2

Answer

-3 *|3-5| = -3 * 2 = -6 = 3

-2 -2 -2

Back

Operations on of Rational #’s for $300

Evaluate the following expression

for b = -2.1

|3 – b| - 2(b + 6) + |b|

Answer

|3 – b| - 2(b + 6) + |b|

= |3 - -2.1| - 2(-2.1 + 6) + |-2.1|

= |5.1| - 2(3.9) + |-2.1|

= 5.1 – 7.8 + 2.1

= -0.6

Back

Operations on of Rational #’s for $400

Add the following two Matrices:

-2.3 3.0 -5.3 2.1 9

1.2 5.4 -7.2 3.2 10.2

6.7 -0.3 -1.5 9.8 7.7

6.4 6.6 -1.6 3.3 -1

7.6 5.0 -7.1 0.1 2.5 3.4 -1.2 3.97.6 -4.3 -6.1 -2.7 4.4 4.6 -10 8.3-7.9 -8.2 -1.1 5.6

+

Answer

The matrices can not be added because they are not the same size. The first is a 4x5, the second is a 5x4

Back

Operations on of Rational #’s for $500

Add the following three Matrices:

-2 7

5 -1

0 6

6 -4

2 -6

-4 -8

9 7

7 -3

3 9

+ + =

Answer

Back

13 10

14 -10

-1 7