Difference between revisions of "2006 iTest Problems/Problem 12"

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<math>\text{(A) }\frac{1}{6!}\qquad \text{(B) }\frac{1}{7!}\qquad \text{(C) }\frac{1}{8!}\qquad \text{(D) }\frac{1}{9!}\qquad \text{(E) }\frac{1}{10!}\qquad \text{(F) }\frac{1}{11!}\qquad\\ \\ \text{(G) }\frac{1}{12!}\qquad \text{(H) }\frac{2}{8!}\qquad \text{(I) }\frac{2}{10!}\qquad \text{(J) }\frac{2}{12!}\qquad \text{(K) }\frac{1}{20!}\qquad \text{(L) }\text{none of the above}\qquad</math>
 
<math>\text{(A) }\frac{1}{6!}\qquad \text{(B) }\frac{1}{7!}\qquad \text{(C) }\frac{1}{8!}\qquad \text{(D) }\frac{1}{9!}\qquad \text{(E) }\frac{1}{10!}\qquad \text{(F) }\frac{1}{11!}\qquad\\ \\ \text{(G) }\frac{1}{12!}\qquad \text{(H) }\frac{2}{8!}\qquad \text{(I) }\frac{2}{10!}\qquad \text{(J) }\frac{2}{12!}\qquad \text{(K) }\frac{1}{20!}\qquad \text{(L) }\text{none of the above}\qquad</math>
  
(Clarification: the <math>\text{nth}</math> question has <math>n</math> answer choices, where <math>n</math> goes from <math>1</math> to <math>20</math>)
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(Clarification: the <math>n\text{th}</math> question has <math>n</math> answer choices, where <math>n</math> goes from <math>1</math> to <math>20</math>)
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==Solution==
 
==Solution==

Revision as of 23:13, 3 November 2023

Problem

What is the highest possible probability of getting $12$ of these $20$ multiple choice questions correct, given that you don't know how to work any of them and are forced to blindly guess on each one?

$\text{(A) }\frac{1}{6!}\qquad \text{(B) }\frac{1}{7!}\qquad \text{(C) }\frac{1}{8!}\qquad \text{(D) }\frac{1}{9!}\qquad \text{(E) }\frac{1}{10!}\qquad \text{(F) }\frac{1}{11!}\qquad\\ \\ \text{(G) }\frac{1}{12!}\qquad \text{(H) }\frac{2}{8!}\qquad \text{(I) }\frac{2}{10!}\qquad \text{(J) }\frac{2}{12!}\qquad \text{(K) }\frac{1}{20!}\qquad \text{(L) }\text{none of the above}\qquad$

(Clarification: the $n\text{th}$ question has $n$ answer choices, where $n$ goes from $1$ to $20$)

Solution