What's the chance a HBeAg positive mother passes HBV to her child?

If you test positive for HBeAg when you are pregnant, it can increase the risk of infection in your baby at the time of birth. The best way to prevent infection in your baby once you have tested positive is to administer the hepatitis B and the hepatitis B immune globulin vaccination within 12 hours of your delivery. The best way to ensure the risk of infection goes down is to screen for the same during each pregnancy. Also, your baby's doctor will have to provide for the fact that your baby's immunity will be extremely low at the time of birth and soon after, and hence keep the baby under constant observation. I found this article very informative https://www.cdc.gov/hepatitis/hbv/pdfs/hepbperinatal-protectwhenpregnant.pdf