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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?
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.
Full Transcript
- 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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