Two generic coins beside three unlettered event cards. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Pairwise products do not fix the triple intersection
Toss two independent fair coins. Define A as first coin heads, B as second coin heads and C as the coins showing the same side. Each event has probability one-half. Every pair has probability one-quarter, so each pair of events is independent.
List the four equally likely elementary outcomes
| Coins | Events occurring |
|---|---|
| HH | A, B, C |
| HT | A only |
| TH | B only |
| TT | C only |
The triple intersection is 1/4, not (1/2)³ = 1/8. The three events therefore are not mutually independent. Their union is certain, because at least one of the listed events occurs in every elementary outcome.
Enter the observed structure explicitly
In known-intersection mode of the three-event calculator, enter marginals 50%, pairs 25% and triple 25%. The tool gives union 100%, exactly one 75%, exactly two zero and all three 25%. Switching to mutual-independence mode changes the model rather than correcting this valid table.
Do not extend a two-event check too far
A pairwise independence check can be useful, but cannot establish the joint behavior of a larger family. Read the eight-atom guide for the full feasibility test. The existing Conditional Probability Calculator only checks two-event relationships and makes no claim about an unentered third event.
Check the model behind your result
Use the Probability of 3 Events Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26