After sending a booklet to print, after client approval, I noticed a typo that was my fault. The client supplied the text but in the design process it was edited and I have misspelt an email address. The client was given proofs and didn't spot it but they haven't received the print version, yet. I feel terrible even though the client is unaware of the issue and may never spot it, but should I email them to explain and offer a discount, or should I wait on them contacting me?
Update: I've contacted my client to notify them of the typo and haven't yet heard back, but feel much better being honest with them. I offered two solutions thanks to the below answers so hopefully this will be resolved soon. Thanks for your input everyone!