The joint probability table shows same-bit correlation while each single bit remains uncertain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Only two joint outcomes have probability
The joint measurement distribution has probability one half on zero-zero and one half on one-one. The crossed outcomes have probability zero.
outcome∣0,0⟩∣0,1⟩∣1,0⟩∣1,1⟩P210021
The bit values always match in this basis
Add the rows where the two bit values match. The same-bit probability is one, even though each individual bit is still uncertain.
Psame=21+21=1
The table separates joint and marginal facts
The joint table says both bits match. It does not say either single qubit had a known value before measurement.