Difference between revisions of "2003 AMC 12A Problems/Problem 24"
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If <math>A</math> and <math>B</math> meet, their paths connect <math>(0,0)</math> and <math>(5,7).</math> There are <math>\binom{12}{5}=792</math> such paths, so the probability is <math>\frac{792}{2^{6}\cdot 2^{6}} \approx 0.20 \Rightarrow \boxed{C}</math> | If <math>A</math> and <math>B</math> meet, their paths connect <math>(0,0)</math> and <math>(5,7).</math> There are <math>\binom{12}{5}=792</math> such paths, so the probability is <math>\frac{792}{2^{6}\cdot 2^{6}} \approx 0.20 \Rightarrow \boxed{C}</math> | ||
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| + | == See Also == | ||
| + | |||
| + | {{AMC12 box|year=2003|ab=A|num-b=23|after=25}} | ||
Revision as of 12:47, 28 February 2010
Problem
Objects 
and 
move simultaneously in the coordinate plane via a sequence of steps, each of length one. Object starts at 
and each of its steps is either right or up, both equally likely. Object starts at 
and each of its steps is either to the left or down, both equally likely. Which of the following is closest to the probability that the objects meet?
Solution
If and meet, their paths connect and 
There are 
such paths, so the probability is 
See Also
| 2003 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 23 |
Followed by 25 |
| 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 | |
| All AMC 12 Problems and Solutions | |
