TOKYO—Before American gymnast Jade Carey took the floor for her unexpected performance in the women’s Olympic all-around final on Thursday, she talked to her teammate, Simone Biles, whose exit from the competition meant Carey got the chance to fill her spot. “She told me, ‘Good luck,’ and go out there, do the best I can and have fun,” Carey said. Carey finished in eighth place, a result she said she was proud of given that just the day before she didn’t even know she would be competing. Biles and other teammates watched from the stands and cheered her on. “I feel really proud of myself for how I was able to step in at the last minute and compete,” Carey said. Biles was scratched from the team finals on Tuesday after she got lost in the air on a vault. She announced Wednesday she would not compete in the individual …