Difference between revisions of "2025 AIME I Problems/Problem 13"
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| + | ==Problem== | ||
| + | Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws <math>25</math> more lines segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting these two points. Find the expected number of regions into which these <math>27</math> line segments divide the disk. | ||
| + | |||
| + | ==See also== | ||
| + | {{AIME box|year=2025|num-b=12|num-a=14|n=I}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Revision as of 21:08, 13 February 2025
Problem
Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 
more lines segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting these two points. Find the expected number of regions into which these 
line segments divide the disk.
See also
| 2025 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
