Why did ''bloody'' mary I give up the throne to elizabeth on her deathbed?

mary was catholic and wanted to eradicate all protestents from the british isles from what i understand and return england to its catholic roots before the split by henry 8th.....so i dont get why would she give up the throne to a protestant monarch who supported the church of england,elizabeth becoming queen would obviously keep england as a non catholic nation and contradict all mary had done in her short reign