View by Category

Loading...

PPT – Learn to find the probabilities of independent and dependent events' PowerPoint presentation | free to view

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Learn to find the probabilities of independent

and dependent events.

Vocabulary

independent events dependent events

Events are independent events if the occurrence

of one event does not affect the probability of

the other. Events are dependent events if the

occurrence of one does affect the probability of

the other.

Additional Example 1 Classifying Events as

Independent or Dependent

Determine if the events are dependent or

independent. A. getting tails on a coin toss and

rolling a 6 on a number cube B. getting 2 red

gumballs out of a gumball machine

Tossing a coin does not affect rolling a number

cube, so the two events are independent.

After getting one red gumball out of a gumball

machine, the chances for getting the second red

gumball have changed, so the two events are

dependent.

Try This Example 1

Determine if the events are dependent or

independent. A. rolling a 6 two times in a row

with the same number cube B. a computer randomly

generating two of the same numbers in a row

The first roll of the number cube does not affect

the second roll, so the events are independent.

The first randomly generated number does not

affect the second randomly generated number, so

the two events are independent.

(No Transcript)

Additional Example 2A Finding the Probability of

Independent Events

Three separate boxes each have one blue marble

and one green marble. One marble is chosen from

each box. A. What is the probability of choosing

a blue marble from each box?

The outcome of each choice does not affect the

outcome of the other choices, so the choices are

independent.

Multiply.

P(blue, blue, blue)

0.125

Additional Example 2B Finding the Probability of

Independent Events

B. What is the probability of choosing a blue

marble, then a green marble, and then a blue

marble?

Multiply.

P(blue, green, blue)

0.125

Additional Example 2C Finding the Probability of

Independent Events

C. What is the probability of choosing at least

one blue marble?

Think P(at least one blue) P(not blue, not

blue, not blue) 1.

P(not blue, not blue, not blue)

0.125

Multiply.

Subtract from 1 to find the probability of

choosing at least one blue marble.

1 0.125 0.875

Try This Example 2A

Two boxes each contain 4 marbles red, blue,

green, and black. One marble is chosen from each

box. A. What is the probability of choosing a

blue marble from each box?

The outcome of each choice does not affect the

outcome of the other choices, so the choices are

independent.

Multiply.

P(blue, blue)

0.0625

Try This Example 2B

Two boxes each contain 4 marbles red, blue,

green, and black. One marble is chosen from each

box. B. What is the probability of choosing a

blue marble and then a red marble?

Multiply.

P(blue, red)

0.0625

Try This Example 2C

Two boxes each contain 4 marbles red, blue,

green, and black. One marble is chosen from each

box. C. What is the probability of choosing at

least one blue marble?

Think P(at least one blue) P(not blue, not

blue) 1.

P(not blue, not blue)

0.5625

Multiply.

Subtract from 1 to find the probability of

choosing at least one blue marble.

1 0.5625 0.4375

To calculate the probability of two dependent

events occurring, do the following 1. Calculate

the probability of the first event. 2. Calculate

the probability that the second event would

occur if the first event had already occurred.

3. Multiply the probabilities.

Additional Example 3A Find the Probability of

Dependent Events

The letters in the word dependent are placed in a

box. A. If two letters are chosen at random, what

is the probability that they will both be

consonants?

P(first consonant)

Additional Example 3A Continued

If the first letter chosen was a consonant, now

there would be 5 consonants and a total of 8

letters left in the box. Find the probability

that the second letter chosen is a consonant.

P(second consonant)

Multiply.

Additional Example 3B Find the Probability of

Dependent Events

B. If two letters are chosen at random, what is

the probability that they will both be consonants

or both be vowels?

There are two possibilities 2 consonants or 2

vowels. The probability of 2 consonants was

calculated in Example 3A. Now find the

probability of getting 2 vowels.

Find the probability that the first letter chosen

is a vowel.

P(first vowel)

If the first letter chosen was a vowel, there are

now only 2 vowels and 8 total letters left in the

box.

Additional Example 3B Continued

Find the probability that the second letter

chosen is a vowel.

P(second vowel)

Multiply.

The events of both consonants and both vowels are

mutually exclusive, so you can add their

probabilities.

P(consonant) P(vowel)

Try This Example 3A

The letters in the phrase I Love Math are placed

in a box. A. If two letters are chosen at random,

what is the probability that they will both be

consonants?

P(first consonant)

Try This Example 3A Continued

If the first letter chosen was a consonant, now

there would be 4 consonants and a total of 8

letters left in the box. Find the probability

that the second letter chosen is a consonant.

P(second consonant)

Multiply.

Try This Example 3B

B. If two letters are chosen at random, what is

the probability that they will both be consonants

or both be vowels?

There are two possibilities 2 consonants or 2

vowels. The probability of 2 consonants was

calculated in Try This 3A. Now find the

probability of getting 2 vowels.

Find the probability that the first letter chosen

is a vowel.

P(first vowel)

If the first letter chosen was a vowel, there are

now only 3 vowels and 8 total letters left in the

box.

Try This Example 3B Continued

Find the probability that the second letter

chosen is a vowel.

P(second vowel)

Multiply.

The events of both consonants and both vowels are

mutually exclusive, so you can add their

probabilities.

P(consonant) P(vowel)

Lesson Quiz

Determine if each event is dependent or

independent. 1. drawing a red ball from a bucket

and then drawing a green ball without replacing

the first 2. spinning a 7 on a spinner three

times in a row 3. A bucket contains 5 yellow and

7 red balls. If 2 balls are selected randomly

without replacement, what is the probability

that they will both be yellow?

dependent

independent

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

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

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

Copyright 2014 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2014 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Learn to find the probabilities of independent and dependent events'" 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!