Dween
Joined: Jan 24, 2010
• Posts: 339
February 8th, 2014 at 7:55:31 AM permalink
The Spanish teacher at my school showed me a test that was divided into various sections. Some matching, some fill-in-the-blank, some word banks, etc. Somehow, this student scored a zero on the entire test. What struck me is that they were very unlucky to get nothing right in any section, but it made me think of this question specifically:

In a matching section of a test, with 7 questions and 7 answers, what are the chances of getting exactly zero correct when choosing randomly?

I feel like I should be able to answer this question on my own, but am not sure where to start. Depending on the first few choices made, it can make it either impossible or 100% certain that a right answer may fall on the last choice(s).
-Dween!
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
February 8th, 2014 at 8:17:12 AM permalink

You're looking for "derangements," the number of permutations of a list where no item is in its original position. Coincidentally, the example given on Wikipedia also involves test taking:
http://en.wikipedia.org/wiki/Derangement.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
boymimbo
Joined: Nov 12, 2009
• Posts: 5994
February 8th, 2014 at 8:24:18 AM permalink
I thought the answer was (6/7)^7 = 33.9917%
----- You want the truth! You can't handle the truth!
wudged
Joined: Aug 7, 2013
• Posts: 998
February 8th, 2014 at 8:28:17 AM permalink
Quote: boymimbo

I thought the answer was (6/7)^7 = 33.9917%

That would be the case if each answer was independent. You could potentially "force" a correct answer even though the first 6 were wrong.

I guess you could also have an exceptionally..talented...student who matches an answer to a question more than once...
boymimbo
Joined: Nov 12, 2009