Difference between revisions of "2006 iTest Problems/Problem 12"
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==Solution== | ==Solution== | ||
− | The highest probability occurs when the first <math>8</math> problems are correct. The probability is thus <cmath>\frac{1}{1}\cdot\frac{1}{2}\cdot\frac{1}{3}\dots\frac{1}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\dots\frac{18}{19}\cdot\frac{19}{20}</cmath> This, when simplified, gives <cmath>\frac{1}{7!\cdot20}</cmath> Which is in none of the answer choices, so the answer is <math>\boxed{ | + | The highest probability occurs when the first <math>8</math> problems are correct. The probability is thus <cmath>\frac{1}{1}\cdot\frac{1}{2}\cdot\frac{1}{3}\dots\frac{1}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\dots\frac{18}{19}\cdot\frac{19}{20}</cmath> This, when simplified, gives <cmath>\frac{1}{7!\cdot20}</cmath> Which is in none of the answer choices, so the answer is <math>\boxed{\text{(L) }\text{none of the above}}</math> |
==See Also== | ==See Also== | ||
{{iTest box|year=2006|num-b=11|num-a=13|ver=[[2006 iTest Problems/Problem U1|U1]] '''•''' [[2006 iTest Problems/Problem U2|U2]] '''•''' [[2006 iTest Problems/Problem U3|U3]] '''•''' [[2006 iTest Problems/Problem U4|U4]] '''•''' [[2006 iTest Problems/Problem U5|U5]] '''•''' [[2006 iTest Problems/Problem U6|U6]] '''•''' [[2006 iTest Problems/Problem U7|U7]] '''•''' [[2006 iTest Problems/Problem U8|U8]] '''•''' [[2006 iTest Problems/Problem U9|U9]] '''•''' [[2006 iTest Problems/Problem U10|U10]]}} | {{iTest box|year=2006|num-b=11|num-a=13|ver=[[2006 iTest Problems/Problem U1|U1]] '''•''' [[2006 iTest Problems/Problem U2|U2]] '''•''' [[2006 iTest Problems/Problem U3|U3]] '''•''' [[2006 iTest Problems/Problem U4|U4]] '''•''' [[2006 iTest Problems/Problem U5|U5]] '''•''' [[2006 iTest Problems/Problem U6|U6]] '''•''' [[2006 iTest Problems/Problem U7|U7]] '''•''' [[2006 iTest Problems/Problem U8|U8]] '''•''' [[2006 iTest Problems/Problem U9|U9]] '''•''' [[2006 iTest Problems/Problem U10|U10]]}} |
Latest revision as of 23:43, 3 November 2023
Contents
Problem
What is the highest possible probability of getting of these
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?
(Clarification: the question has
answer choices, where
goes from
to
)
Solution
The highest probability occurs when the first problems are correct. The probability is thus
This, when simplified, gives
Which is in none of the answer choices, so the answer is
See Also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem 11 |
Followed by: Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • U1 • U2 • U3 • U4 • U5 • U6 • U7 • U8 • U9 • U10 |