Difference between revisions of "2019 AIME I Problems/Problem 5"
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If this algebra seems intimidating, you can watch a nice pictorial explanation of this by On The Spot Stem. | If this algebra seems intimidating, you can watch a nice pictorial explanation of this by On The Spot Stem. | ||
https://www.youtube.com/watch?v=XBRuy3_TM9w | https://www.youtube.com/watch?v=XBRuy3_TM9w | ||
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+ | ==Solution 2== | ||
==See Also== | ==See Also== | ||
{{AIME box|year=2019|n=I|num-b=4|num-a=6}} | {{AIME box|year=2019|n=I|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 18:13, 10 March 2020
Contents
Problem 5
A moving particle starts at the point and moves until it hits one of the coordinate axes for the first time. When the particle is at the point
, it moves at random to one of the points
,
, or
, each with probability
, independently of its previous moves. The probability that it will hit the coordinate axes at
is
, where
and
are positive integers. Find
.
jaskdfjskdjfksdfj
Solution
One could recursively compute the probabilities of reaching as the first axes point from any point
as
for
and the base cases are
for any
not equal to one.
We then recursively find
so the answer is
.
If this algebra seems intimidating, you can watch a nice pictorial explanation of this by On The Spot Stem. https://www.youtube.com/watch?v=XBRuy3_TM9w
Solution 2
See Also
2019 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.