The Infinite Monkey Theorem
The Infinite Monkey Theorem
If four monkeys decide to try the New York State Algebra Exam, one will surely succeed.
The Infinite Monkey Theorem states: “a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text,” including Shakespeare's Hamlet; one can also replace the infinite time given to a single monkey by an infinite number of monkeys who are given a finite time. According to a recent article in the Medium, entitled “Guessing C For Every Answer Is Now Enough To Pass The New York State Algebra Exam”, of four monkeys trying to pass the New York State Algebra Exam, in 2022, one will surely succeed… in one go.
The exam consists of 24 multiple choice (MC) questions, four choices each, “A-B-C-D”, and 13 constructed response (CR) problems. MCs are 2 points each; CR’s price varies from 2 through 4. The passing grade, the one that gets you a high school diploma, is 17 points.
Now, we set to prove the statement in the sub-title. We recruit a group of four monkeys - Anna, Ben, Chris, and Diana. We train them to always make the same choice in MPs and ignore the CRs. Anna is trained to always check A, Ben - B, Chris - C, and Diana - D. You would think this strategy is no better than a random choice that would give you a mere 12% chance of reaching the 17-point bounty. Not so fast…
In the year in question, 2022, the set of correct answer to the MC questions consisted of 5 As, 5 Bs, 5 Ds, but 9 Cs. Hence our Chris the Monkey, who answered C to each of the 24 multiple choice questions and returned to his coco palm tree before the constructed response problems were assigned, will be recorded as having a satisfactory command in algebra for a 10th grader, in the great State of New York. Q.E.D. 1
It bears mentioning that prior to 2022, the passing grade was 26, and our four monkeys would not have a chance back then. This year, however, the New York State Education Department decided to lower the bar to 17, hence Chris’s triumph.
But one needn’t think that the more ridiculous the exams become, the better one’s chances are to convince others to improve them. Maybe. But maybe not. Maybe all this is happening by design. Maybe the Social Justice Warriors are staring getting tired of repeating the correlation-causation fallacy of “better scores in richer districts → test measures the money spent on the test prep”, and decided for a new strategy: reduce the tests to a parody of the former selves and abolish them later. (In the UMB context, the proctored ALEKS transmogrification to an un-proctored comes to mind.) Who is the “infinite monkey” now? Maybe it’s our poor students deprived of any career guidance and duped infinitely.
In fact, choosing the same letter for all 24 MC questions, and, in addition, answering correctly to two 4-point MCs will give you 18 points minimum, one point over the passing grade. In that case, Anna, Ben, and Diana will join Chris in his triumph. A sample 4-pointer looks as follows:
