Probability of Simple Events Return to Table of Contents Slide 7 - - PDF document

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Slide 1 / 66 Slide 2 / 66 Geometry Probability 2015-10-28 www.njctl.org Slide 3 / 66 Slide 4 / 66 Table of Contents Throughout this unit, the Standards for Mathematical Practice are used. Click on a topic to go to that section MP1:

SLIDE 1

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Geometry

Probability

2015-10-28 www.njctl.org

Slide 3 / 66 Table of Contents

Probability of Simple Events Probability and Length Probability and Area

Click on a topic to go to that section

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Throughout this unit, the Standards for Mathematical Practice are used. MP1: Making sense of problems & persevere in solving them. MP2: Reason abstractly & quantitatively. MP3: Construct viable arguments and critique the reasoning of

thers.

MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for & make use of structure. MP8: Look for & express regularity in repeated reasoning. Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used. If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.

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Probability of Simple Events

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A sample space is a set of ALL possible outcomes for an activity

r experiment.

A sample space is usually denoted using set notation {...} and the possible outcomes are listed as elements in the set {a, b, c, ... z}.

Sample Space

SLIDE 2

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Find the sample space in the box below each activity. {yellow, blue, red, green} H = heads T = tails {HH, HT, TH, TT} {1, 2, 3, 4, 5, 6} {yellow, green, red}

{(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2)(4,3) (4,4) (4,5)(4,6) (5,1) (5,2)(5,3) (5,4) (5,5)(5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}

Sample Space

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If the outcomes in a sample space are equally likely to occur, the theoretical probability of an event P(event) is a numerical value from 0 to 1 that measures the likelihood of an event. You can write the probability of an event as a ratio, decimal or a percent. P(event) = number of favorable outcomes number of possible outcomes · An event with a probability close to 0 is unlikely to occur. · An event with a probability close to 1 is likely to occur. · An event with a probability of 0.5 is just as likely to occur as not.

Impossible Certain Equally Likely to Occur

r not Occur

0 less likely 0.5 more likely 1

Theoretical Probability Slide 9 / 66

There are 7 red marbles and 3 green marbles in a bag. One marble is chosen at random. Write the probability that a green marble is chosen. P(Green)

Write as a fraction Write as a decimal Write as a percent

Non - Geometric Examples Slide 10 / 66

P(card) = 1/ 52

Suppose you choose a card from the deck. What is .... P(Heart) = P(3) = P(4 of Spades) = __

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P(2) = ___ P(even) = _ P(prime) = _ P(> 4) = ___

Probability

2. Find the probability of

each event.

1. Find the sample space for the

activity below.

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2. Find the probability of

each event. P(green) = _ P(orange) = _

1. Find the sample space for

the activity below.

Probability

SLIDE 3

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P(heads) = _ P(tails) = _

2. Find the probability of

each event.

1. Find the sample space for the

activity below.

Probability Slide 14 / 66

1 A multiple choice question has 14 possible answers,

nly one of which is correct. Is it "unlikely" to answer

a question correctly if a random guess is made? Yes No

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2 What is the sample space for flipping a coin twice? A HT, TH B HH, HT, TH, TT C HH, HT, TT D HH, TT, HT, HT

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3 What is the sample space for flipping a coin 3 times? A HHH, TTT, THT, HTH, HHT, TTH, HTH B HHH, HTT, HTH, TTT, HTT, THH, HHT, THT C HTT, THT, HTH, HHH, TTH, TTT D HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

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4 On a multiple choice test, each question has 4 possible

answers. If you make a random guess on the first

question, what is the probability that you are correct?

A

4 B

1 C

1/4

D

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5 A die with 12 sides is rolled. What is the probability of rolling a number less than 11? A 1/12 B 10 C 5/6 D 11/12

SLIDE 4

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6 What is the probability of rolling a number greater than 2 on a number cube? A 1/6 B 1/3 C 1/2 D 2/3

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7 What is the probability of randomly choosing a science book from a shelf that holds 3 mystery books, 5 science books and 4 nature books? A 1/4 B 1/3 C 5/12 D 7/12

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8 A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? A 1/3 B 3/16 C 1/13 D 1/7

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We have evaluated probabilities by counting the number of favorable outcomes and dividing that number by the total number of possible outcomes. In the rest of this unit, you will use a related process in which the division involves geometric measures such as length or

area. This process is called geometric probability.

click to reveal

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Probability and Length

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Slide 24 / 66 Using Segments to Find Probability

A B C D Point K on AD is chosen at random. The probability that K is on BC is the ratio of the length of BC to the length of AD. P(K on BC) = BC AD Fill in the blanks. P(K on AC) = P(K on AB) = AD

SLIDE 5

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2 3 4 5 6 7 8 9 10 11 12 13 14

S Q R T Point H on ST is selected at random. What is the probability that H lies

n SR?

Step 1: Find the length of each segment. length of SR = length of ST =

Using Segments to Find Probability Slide 26 / 66

2 3 4 5 6 7 8 9 10 11 12 13 14