It's okay to eat a burger with a little pink as long as the burger has been cooked to a minimum internal temperature of at least 160 F, throughout the burger to kill bacteria such as E. coli.
Color is not always a reliable indicator of the burger being safe to eat and some burgers that are fully cooked can also remain slightly pink, which is safe to eat.
Relying just on the color like medium rare can be risky as the ground meat can contain bacteria throughout the burger.
But as long as the burger has been cooked to at least 160 F then it's safe to eat the burger with a little pink.
Sometimes a fully cooked burger can look pink due to a reaction with the heat sources, such as on gas grills or other specific cooking conditions.
Just make sure the burger is fully cooked as eating undercooked burgers can cause serious foodborne illnesses in some cases.
And unlike steak, which you can eat rare, ground beef for burgers also requires thorough cooking, due to pathogens on the surface of the meat, which are also distributed throughout the meat.
When grilling burgers or cooking burgers you can also use the 5 6 7 rule for burgers which is a guideline for grilling burgers, which helps you achieve consistent doneness of the grilled burger, which is based on cooking time per side.
This is assuming you have a 1/2 inch to 3/4 inch thick hamburger patty, over medium heat.
The 5 6 7 rule for burgers suggests that you grill the burgers for 5 minutes per side for rare to medium rare, 6 minutes for medium and grill the burgers for 7 minutes for well done.
This helps to ensure that you get a nice juicy burger on the grill without needing a thermometer.
5 minutes of cooking per side when grilling the burgers, produces a burger that is rare to medium rare.
6 minutes of cooking per side produces a burger that is medium done.
And 7 minutes of cooking per side produces a burger on the grill that is well done.
So if you want your grilled burger to be rare to medium rare, you would grill the burgers for 5 minutes per side.
If you want your grilled burger to be medium done, you would grill your burger for 6 minutes per side.
And if you want your grilled burger to be done fully, then you would grill your burger for 7 minutes per side.
Also don't press down on the burgers when grilling them, to prevent drying the burgers out.
And the 5 6 7 rule for grilling burgers also works best on a grill that is preheated to 350 F to 400 F with 80/20 ground beef.
And some interpretations of the 5 6 7 rule, define it as 5 minutes on one side, 6 minutes on the other side and a 7 minute rest period for maximum juiciness.