The Selective College Correlation
Two fair six-sided dice are rolled independently, giving $(A, B)$. A pair is admitted only if $A + B \ge 10$. Among admitted pairs (each of the 36 outcomes equally likely beforehand), what is the correlation between $A$ and $B$? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Correlation of Sum and Difference 2.0/10
- Variance of Two Dice 2.0/10
Source: Berkson's paradox (Berkson 1946); setup original. Statement written for AxiomIQ.