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Statistics, Data, and Probability I Videos 30 videos

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CAHSEE Math 6.5 Statistics, Data, and Probability I 189 Views


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Description:

Statistics, Data, and Probability I: Drill Set 6, Problem 5. What is the probability that the man will first pick a brown eyeball and then a white eyeball?

Language:
English Language

Transcript

00:03

Here's a shmoopy question for you...

00:05

There are six brown, four blue, four green,

00:08

and ten white eyeballs in an unmarked duffel bag recently found near the Jersey shore.

00:14

A well-dressed man with a loud tie, without looking,

00:17

must choose one at random and then pick a second eyeball.

00:21

What is the probability that the man will first pick a brown eyeball, and then pick a white eyeball?

00:27

And here are our potential answers:

00:31

OK, so what is this question asking, anyway?

00:34

Other than... "what in the world is going on here?"

00:37

By the way... if the thought of touching eyeballs doesn't gross you out, you may want to consider

00:41

the field of optometry as a career choice -- it can be quite lucrative.

00:45

Anyway, what we have here is a two-step probability problem.

00:48

We are being tested in large part on whether we can recognize DEPENDENT and INDEPENDENT events.

00:54

In this case, we have to feel that red light flashing and recognize that these events are DEPENDENT...

01:00

...because after taking out the first eyeball... and not putting it back... our total will

01:05

diminish by one.

01:07

So the total eyeballs are: 6 plus 4 plus 4 plus 10... or 24.

01:14

There are 6 brown eyeballs, so the odds of first choosing a brown from the duffel bag

01:19

are 6 in 24... or 1 in 4 once that fraction gets... melted down...

01:25

We are now left with 23 eyeballs... and note that we only have 5 brown ones left.

01:31

So the well-dressed man picks again, hoping for a white eyeball...

01:34

...his odds are 10 in 23 here because there are 10 white eyeballs still in the bag...

01:40

But the question asks what are the odds of BOTH of these things happening...

01:44

...so when we cover two linked events, we multiply them to get the TOTAL odds...

01:49

...we have one over four times 10 over 23 to get 10 over 92 which reduces to 5 over 46.

01:57

So our answer is choice B.

01:59

Should we take a vote to make sure there's a consensus on the right answer?

02:02

Looks like the eyes have it.

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