View by Category

Loading...

PPT – Chapter 1: Basic Concepts in Probability PowerPoint presentation | free to view - id: 1c9d9-M2QyY

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Chapter 1 Basic Concepts in Probability

- It will include the following topics/sections
- 1.1 Sample Spaces, Events, and Probabilities
- 1.2 Simulations
- 1.3 Complementary Events and Mutually Exclusive

Events - 1.4 Some Probability Rules

1.1 Sample Spaces, Events, and Probabilities

- A sample space, S, is defined as the set of all

possible outcomes of an experiment. If the

outcomes in S are equally likely, we call S an

equally probable sample space. Any subset of S is

called an event.

1.1 Sample Spaces, Events, and Probabilities

- Example 1If a box contains three balls numbered

1, 2, 3 and we draw one ball from the box in such

a way that each of the three balls are equally

likely to be selected, then 1, 2, 3 is an

equally probable sample space and - For this experiment odd, even is also a

sample space but not an equally probable sample

space since an odd outcome is twice as likely as

an even outcome.

1.1 Sample Spaces, Events, and Probabilities

- Definition 1

1.1 Sample Spaces, Events, and Probabilities

- Example 2 Box I contains balls numbered 1, 2, 3

and box II contains 2, 3 and 4. One ball is

selected at random from each box. Then, the

sample space is S(1, 2), (1, 3), (1, 4), (2,

2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4),

where the first number in each order pair denotes

the number on the ball drawn from box I and the

second number in each ordered pair denotes the

number on the ball drawn from box II. This is the

set of all possible outcomes of this experiment,

and S is an equally probable sample space.

Consider the event A where Asum of digits on

the selected balls is an even number. Then

A(1, 3),(2, 2),(2, 4),(3, 3). Hence P(A)4/9.

(Why?)

1.1 Sample Spaces, Events, and Probabilities

- Example 3 Two red blocks and two green blocks

are arranged at (all the possible arrangements

are equally likely) in a row. Let Athere is

exactly one green block between two red blocks.

Find P(A). - Hint S(RRGG),(RGRG),(RGGR),(GGRR),(GRGR),(GRRG

), and S is equally probable sample space.

Why?

1.1 Sample Spaces, Events, and Probabilities

- Example 4 A box contains four balls numbered 1,

2, 3, 4. Two chips are drawn, at random, without

replacement, from the box. Let Alargest number

selected is 3. Find P(A).

1.1 Sample Spaces, Events, and Probabilities

- Homework / Class Exercises (Section 1.6, page 19)
- Do problems 2, 3, 6
- Enjoy your homework, and have a

wonderful day!

1.2 Simulations

- There are situations where either there is

no an analytic solution or we dont know to find

the analytic solution to a probability problem.

In these cases we can estimate P(A) by long-run

proportion of the times that A occurs. In other

words, we simulate the experiment. For this

course, we will use a random number target (see

page 6) to carry out these simulations.

1.2 Simulations

- Example 1 Box I contains balls numbered 1,

2, 3 and box II contains balls numbered 2, 3, 4.

One ball is selected at random from each box.

Consider the event Athe sum of the digits on

the selected balls is an even number. To

demonstrate the simulation procedure we will

estimate P(A) in this example.

1.2 Simulations

- Let us simulate this experiment 20 times

(why?). For the drawing from box I, we select

a number from the random number target until we

get either a 1, 2, or 3. So for this drawing,

4s, 5s, and 6s will be ignored. For the

drawing from box II, we select a number from the

random number target until we get either a 2, 3,

or 4. In this case 1, 5, and 6 are ignored.

1.2 Simulations

- Simulation Number

1.2 Simulations

- Simulation Number

1.2 Simulations

- The estimate of P(A) is the proportion of

times which A occurs which is 8/20 or 0.4. This

is not P(A). We have already evaluated P(A) to be

4/9. The value of 0.4 is an estimate of P(A)

based on the simulations.

1.2 Simulations

- Example 2 Problem 9, section 1.6
- Describe how to estimate P(A) for the above

example without ignoring any numbers from the

random number target.

1.2 Simulations

- Homework / Class Exercises (Section 1.6, page

18-20) - Do problems 1, 8
- Enjoy your homework, and have a

wonderful day!

1.3 Complementary Events and Mutually Exclusive

Events

- Definition
- Events A, B are said to be mutually exclusive if

they cannot occur together. - Example 1 Toss a die once. Then the events A1

and 5 are mutually exclusive. Why?

1.3 Complementary Events and Mutually Exclusive

Events

- Definition
- Events A, B are said to be complementary if both

of the following conditions are satisfied - Events A, B are mutually exclusive.
- Events A, B exhaust the sample space in the sense

that every outcome in S is ether in A or in B. - Example 2 Toss a die once. Then the events

Aodd number and Beven number are complementary.

Why?

1.3 Complementary Events and Mutually Exclusive

Events

- Example 3 Suppose that student Meat Loaf takes 5

courses for each of the 8 semester that he is

working on his college degree. Describe the

complementary event to each of the following - Gat least one semester Meat Loaf gets all As,
- HMeat Loaf makes at least one A every

semester,

1.3 Complementary Events and Mutually Exclusive

Events

- Solution (i) This means that Meat Loaf gets 5

As in either 1, 2, 3, 4, 5, 6, 7, or 8

semesters. The complementary event is that he

makes 5 As zero times. So, not Ghe makes less

than 5 As every semester. - (ii) This means that Meat Loaf makes either 1, 2,

3, 4, or 5 As for all eight semesters. The

complementary event is that he makes zero As in

at least one semester. So, not Hhe makes zero

As in at least one semester.

1.3 Complementary Events and Mutually Exclusive

Events

- Exercise Suppose that student Meat Loaf takes 2

courses for each of the 2 semester that he is

working on his college degree. - (a) Describe the sample space.
- (b) Describe the complementary event to each of

the following both in terms of English statement,

and mathematical notation. - Gat least one semester Meat Loaf gets all As,
- HMeat Loaf makes at least one A every

semester,

1.3 Complementary Events and Mutually Exclusive

Events

- Homework / Class Exercises (Section 1.6, page

18-20) - Do problems 10
- Enjoy your homework, and have a

wonderful day!

1.4 Some Probability Rules

- Probabilities satisfy the following rules
- Rule 1 P(A)0 if A is impossible event (Athe

empty set) - Rule 2 P(A)1 of A is certain event (AS)
- Rule 3 P(A)1-P(not A)
- Rule 4 If A and B are mutually exclusive events,

P(A or B)P(A)P(B)

1.4 Some Probability Rules

- Example 1Look Example 1.8 on page 10.
- Choose one letter from English language text.
- Find
- P(vowel is chosen)
- P(consonant is chosen)

1.4 Some Probability Rules

- Homework / Class Exercises (Section 1.6, page

18-20) - Do problems 11, 15
- Enjoy your homework, and have a

wonderful day!

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Chapter 1: Basic Concepts in Probability" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Montgomerycollege University and other schools with their online training by sharing educational presentations for free