Here's what we know from the article: (1) 40 question test, (2) Multiple choice, (3) She passed it with "60 out of 100"
My assumptions:
(1) It's graded on a simple "percentage right" basis, so 24/40 questions necessary right to pass, (2) 4 options for each question
Her score on an individual test is a random variable X following a binomial distribution with 40 trials and chance of 0.25 for each trial. Her chance of passing by guessing randomly, P(X >= 24), is an infinitesimally small 2.826E-6.
The probability that she fails all of the 960 tests, assuming independence of tests, is (1-p)^960. So the probability that she will pass at least one test is:
1 - (1 - p)^960
Plugging in p = 2.826E-6, the chance is still practically 0, so a naive guessing strategy would not work.
However, under the above assumptions, she could practically guarantee her success by combining this guessing strategy with a simple test-taking strategy like eliminating 1 or 2 obviously wrong answers per question, or just remembering the answers to several of the same questions that are probably being recycled from test to test.
just remembering the answers to several of the same questions that are probably being recycled from test to test.
I assumed this is how she did it, but assuming all questions are recycled, 4 options in 40 questions, perfect memory, no knowledge, and a naïve strategy, she should have passed in just 29 tries (1.75 retries per question, 10 initially right, 24 needed). Mastermind isn't that hard a game. So clearly, some assumptions are wrong.
