Multiple choice ...

I am sitting on an airplane at the moment reading XKCD – What IF … Serious Scientific Answers to absurd hypothetical questions. Hitting upon P278 – SAT Guessing. The question “What if everyone who took the SAT, guessed on every multiple choice question. How many perfect scores would there be – Rob Balder”.

In my professional life I have often wanted to ‘force choke’ morons who try and tell me that multi-choice quizzes always guarantee a mark of 25%’. Knowing that the result is a form of compound calculation.

If you have 4 choices per question and 20 questions. It is 1/(4^20) [one divided by 4 that is to the power of 20). The result is 9.09495E-13 … this value is a negative exponent. So to see this number in plainer terms you have to float the decimal point to the left 13 times. Making it a probability of 0.000000000000909495 (which is smaller than a 1 in a zillion chance).
Most commercial multi-choice vendor exams offer around 50 questions; the CCNA finals are an excellent example of this. The probability of 50 lucky guesses is 7.88861E-31 yep 1 in 0.00000000000000000000000000000788861 or frigging unlikely.

If you ever encounter someone who has passed or gained 100% in any certification exam. Its not luck as the probability is greater than the number of humans on this planet; it is based on their ability to read the question and get the right answer.

You may claim that the multi-choice quizzes are easy to guess. We humbly suggest that you wander into a test centre and try one. I have seen hardened geeks wander out with weak bladders, brain injuries and missing the pass mark by a margin. A well written stem will have four answers that all seem plausible but only one that is actually correct if they know the subject and able to read the frigging question.

So, if you do encounter someone who disparages your vendor certification … please feel to attempt a ‘force choke’ on him or her. The alternative is illegal but nevertheless tempting. 

For nerds, the data can be seen here.



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