 BB84 intercept-resend error rate

In ideal BB84 with uniform independent basis choices, intercepting a fraction $q$ of signals, measuring in a random protocol basis and resending that result introduces sifted-key bit error rate $q/4$. Conditional on a retained position, the attacker chose the wrong basis with probability $1/2$; then the receiver disagrees with the original bit with probability $1/2$. The calculation describes one particular attack and does not establish general security.