Difference between revisions of "1991 AIME Problems/Problem 10"
m |
|||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | Two three-letter strings, <math>aaa^{}_{}</math> and <math>bbb^{}_{}</math>, are transmitted electronically. Each string is sent letter by letter. Due to faulty equipment, each of the six letters has a 1/3 chance of being received incorrectly, as an <math>a^{}_{}</math> when it should have been a <math>b^{}_{}</math>, or as a <math>b^{}_{}</math> when it should be an <math>a^{}_{}</math>. However, whether a given letter is received correctly or incorrectly is independent of the reception of any other letter. Let <math>S_a^{}</math> be the three-letter string received when <math>aaa^{}_{}</math> is transmitted and let <math>S_b^{}</math> be the three-letter string received when <math>bbb^{}_{}</math> is transmitted. Let <math>\displaystyle p</math> be the probability that <math>S_a^{}</math> comes before <math>S_b^{}</math> in alphabetical order. When <math>\displaystyle p</math> is written as a fraction in lowest terms, what is its numerator? | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1991|num-b=9|num-a=11}} | |
Revision as of 01:28, 2 March 2007
Problem
Two three-letter strings, 
and 
, are transmitted electronically. Each string is sent letter by letter. Due to faulty equipment, each of the six letters has a 1/3 chance of being received incorrectly, as an 
when it should have been a 
, or as a when it should be an . However, whether a given letter is received correctly or incorrectly is independent of the reception of any other letter. Let 
be the three-letter string received when is transmitted and let 
be the three-letter string received when is transmitted. Let 
be the probability that comes before in alphabetical order. When is written as a fraction in lowest terms, what is its numerator?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 1991 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
