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?
|CAHSEE Math||Statistics, Data, and Probability I|
|Mathematics and Statistics Assessment||Interpreting Categorical and Quantitive Data|
|Statistics and Probability||Probability|
|Statistics, Data Analysis, and Probability 6||Independent and dependent events|
What is the probability that the man will first pick a brown eyeball, and then pick a white eyeball?
And here are our potential answers:
OK, so what is this question asking, anyway?
Other than... "what in the world is going on here?"
By the way... if the thought of touching eyeballs doesn't gross you out, you may want to consider
the field of optometry as a career choice -- it can be quite lucrative.
Anyway, what we have here is a two-step probability problem.
We are being tested in large part on whether we can recognize DEPENDENT and INDEPENDENT events.
In this case, we have to feel that red light flashing and recognize that these events are DEPENDENT...
...because after taking out the first eyeball... and not putting it back... our total will
diminish by one.
So the total eyeballs are: 6 plus 4 plus 4 plus 10... or 24.
There are 6 brown eyeballs, so the odds of first choosing a brown from the duffel bag
are 6 in 24... or 1 in 4 once that fraction gets... melted down...
We are now left with 23 eyeballs... and note that we only have 5 brown ones left.
So the well-dressed man picks again, hoping for a white eyeball...
...his odds are 10 in 23 here because there are 10 white eyeballs still in the bag...
But the question asks what are the odds of BOTH of these things happening...
...so when we cover two linked events, we multiply them to get the TOTAL odds...
...we have one over four times 10 over 23 to get 10 over 92 which reduces to 5 over 46.
So our answer is choice B.
Should we take a vote to make sure there's a consensus on the right answer?
Looks like the eyes have it.