geometric-probability-area
In a continuous uniform sample space a probability equals the measure of the favorable region divided by the measure of the whole — for planar problems, the favorable area over the total area. The decisive move is translating the stated condition (a comparison, a triangle inequality, an obtuse-angle test) into a planar region bounded by lines and circular arcs, then computing its area as a triangle, a rectangle fraction, or a circular sector plus or minus a triangle.
풀이 전략
- Keep the unit-square setup but change the condition from y > x (a triangle, P = 3/4) to an arc boundary to force a sector computation
- Scale the two intervals to different lengths so the sample space is a rectangle rather than a square
- Replace a line-bounded favorable region with one bounded by a circular arc to push the difficulty up a grade
세부 유형 분포 (3)
한 줄을 클릭하면 그 안의 문제를 볼 수 있어요.
- region-area-proportional-probability 14% (5)
Outcomes correspond to sub-regions of a figure and each outcome's probability equals its region's share of the total area; compute the area shares, then combine them (sum, product over independent trials, or parity casework) to answer the question.
- uniform-draw-favorable-region 76% (28)
One or two reals are drawn uniformly from intervals; the condition is translated into a favorable sub-region of the interval, square, or rectangle, and the probability is that region's area over the total — a triangle ratio for line-bounded conditions, a sector plus or minus a triangle for arc-bounded ones.
no figureamc10-2003A-12no figureamc10-2009B-23no figureamc10-2011A-20no figureamc10-2011B-13no figureamc10-2014B-19no figureamc10-2015A-25no figureamc10-2017A-15no figureamc10-2018B-22
amc12-2002A-22no figureamc12-2002B-18no figureamc12-2003B-21no figureamc12-2004A-20no figureamc12-2006A-22no figureamc12-2006B-20no figureamc12-2007B-13no figureamc12-2008B-21no figureamc12-2009B-18no figureamc12-2009B-23no figureamc12-2010B-18no figureamc12-2011B-9no figureamc12-2012A-23no figureamc12-2015A-23no figureamc12-2017A-10no figureamc12-2017B-20no figureamc12-2018A-24no figureamc12-2020B-25no figureamc12-2023B-20no figureamc12-2024A-20 - uniform-cube-volume-region 11% (4)
Three reals are drawn uniformly and independently, so the sample space is a cube rather than a square and the probability is a volume ratio; translate the condition into a solid region — typically a tetrahedron or a pyramid cut from the cube — and compute its volume over the cube's, often exploiting symmetry among the three variables to reduce to one ordered case and multiply back.
더 보기 (연도 추세, 도구 fingerprint, 학년 분포, 전체 문제)
도구 fingerprint (1–17)
학년 분포
- Gr 7 7
- Gr 8 5