MathGoldMedalist
Sign InRegister

Geometric Probability

Lesson · Intermediate

Probability

1 dimension

0≤x≤1 0\le x\le1
P(13<x<12)=12−13=16 P\left(\frac13<x<\frac12\right) = \frac12-\frac13 = \frac16
Geometric probability on a line segment from 0 to 1

2 dimensions

0≤x,y≤1 0\le x,y\le1
P(∣x−y∣≥12)=2×12×122=14 P\left(|x-y|\ge\frac12\right) = 2\times\frac{\frac12\times\frac12}{2} = \frac14
Geometric probability in the unit square

3 dimensions

0≤x,y,z≤1 0\le x,y,z\le1
P(x+y+z≤1)=1⋅1⋅16=16 P(x+y+z\le1) = \frac{1\cdot1\cdot1}{6} = \frac16
Geometric probability in the unit cube for x plus y plus z at most 1
Back to Toolkit