What's the probability of having a false negative pregnancy test when my period is 3 days late?

Not inconceivable: Sorry but pun was intended. While home pregnancy tests are fairly sensitive, some women will have a negative test early on during pregnancy. So if you've been engaging in unprotected sex and your test is negative 3d after being late, then repeat test once you're a week or two late. By 2 wks late or 6wks after last menstrual period, home pregnancy test should be positive if you're pregnant.