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Independent and Dependent Events 7743 Views


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Description:

This video covers both independent and dependent events, although we much prefer independent events. Dependent events are just so dang clingy.

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English Language

Transcript

00:04

Independent and Dependent Events, a la Shmoop. Congratulations! You've been chosen as a contestant

00:15

on that game show where people dress up in silly costumes and try to win prizes.

00:24

You're dressed as Euclid, but the host keeps calling you Gandalf. Go figure.

00:30

To win the car, you have to spin this spinner... And meet two conditions:

00:37

One. You have to spin an odd number on the first spin.

00:42

Two: The sum of the two numbers you spin must be odd.

00:47

This is a little more complicated than Plinko... We want to know if, using the formal definition

00:55

of independenceÉ É events A and B are independent or dependent.

01:06

Before we start, lets define what makes an event independent or dependentÉ

01:11

A dependent event depends on the outcome of a secondary eventÉ

01:19

Éwhile an independent event doesnÕt have to answer to anybody. HeÕs more of a free spirit.

01:48

As the audience cheers you on, let's give this problem a spin.

01:54

Here's a chart of the possible outcomes. The numbers down the side show up on the first

02:02

spin; the numbers across the top show up on the second spin.

02:15

The numbers in the table show the sum of the two spins.

02:21

Nowhere in there is your new car. Don't get your hopes up.

02:35

Since both one and three are odd, the probability of getting an odd number on your first spin

02:40

is good. The probability of A is two out of three.

02:48

It's a little more difficult to spin twice and still have an odd number.

03:04

Since there are 9 total possible outcomes and 4 of them are oddÉ

03:11

The probability of B on its own is four out of nine.

03:18

But remember, the only results that count are the ones that occur when you spin an odd

03:26

number first. The probability of A and B happeningÉ the

03:39

only outcomes that occur in both tablesÉ is two out of nine.

03:44

They don't make these things easy. Maybe you should just take what's behind curtain number

03:51

two. But what we really want to know is if these

03:56

events are independent or dependent. Since the probability of A, two-thirds, times

04:11

the probability of B, four-ninths, which comes out to eight-twenty-sevenths, does NOT equal

04:27

the probability of A and B, which is two-ninths, the events are dependent.

04:38

We can't give you a car, but we can help give you a better grade.

04:44

Which is even better, really. At least with a better grade, you donÕt have to make monthly

04:49

payments.

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