Explore imprecise probability
More than one possible probability.
Adjust the bounds for three outcomes and explore the distributions that satisfy them. What changes when you know less—or when your bounds disagree?
Set your intervals
Each interval is a lower and upper bound for an outcome’s probability.
Use the sliders or type a value between 0 and 1. Each lower bound must be no greater than its upper bound.
The space of possibilities
Every point in the triangle is a probability distribution.
Compatible distributionsExample distribution
Read the triangle
One point, three probabilities
Each corner assigns probability 1 to one outcome. Anywhere inside, the three probabilities add to 1. The shaded region contains all distributions consistent with your intervals.
p(A) + p(B) + p(C) = 1
Think about it
What do the bounds really allow?
Try the presets, then change one bound at a time. Can you make the shaded region shrink to a single point?