Difference between revisions of "2016 UNCO Math Contest II Problems/Problem 6"
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== Problem == | == Problem == | ||
| + | |||
| + | Rock and Roll Forever? | ||
| + | (a) Given the situation in Question <math>5</math>, what is the probability that | ||
| + | Sisyphus must labor forever? That is, if Sisyphus begins with one rock in the valley on his | ||
| + | first morning, what is the probability that the Olympian rocks are never all vaporized? | ||
| + | (b) Suppose that the whims of Zeus obey the following rules instead: a rock will either be | ||
| + | vaporized (with probability 10%), be rolled back down into the valley (with probability 20%), | ||
| + | be split by a thunderbolt into two rocks that are both rolled down into the valley (with probability | ||
| + | 30%), or be split by two thunderbolts into three rocks that are all rolled down into the | ||
| + | valley (with probability 40%). Now what is the probability that Sisyphus must labor forever? | ||
== Solution == | == Solution == | ||
Revision as of 00:36, 20 May 2017
Problem
Rock and Roll Forever?
(a) Given the situation in Question 
, what is the probability that
Sisyphus must labor forever? That is, if Sisyphus begins with one rock in the valley on his
first morning, what is the probability that the Olympian rocks are never all vaporized?
(b) Suppose that the whims of Zeus obey the following rules instead: a rock will either be
vaporized (with probability 10%), be rolled back down into the valley (with probability 20%),
be split by a thunderbolt into two rocks that are both rolled down into the valley (with probability
30%), or be split by two thunderbolts into three rocks that are all rolled down into the
valley (with probability 40%). Now what is the probability that Sisyphus must labor forever?
Solution
See also
| 2016 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
[[Category:]]
