TOKYO — Jade Carey redeemed herself from a disappointing performance in the vault final to come back the next day here at the Tokyo Games and win the gold medal on the floor exercise.

Wearing a red, white and blue leotard that sparkled in the lights of the Ariake Gymnastics Center, she flipped, twisted and danced her way to the top of the podium, performing her highly difficult skills with power and ease.

Italy’s Vanessa Ferrari won silver and two gymnasts tied for bronze: Mai Murakami of Japan and Angelina Melnikova of Russia.

After realizing that she had won, Carey gave her coach, Brian — who is also her father — a big hug. The day before, the two had hugged on the competition floor, but out of sadness.

In the vault final on Sunday, Carey, who is 21 and from Phoenix, tripped during her run-up to her first vault. She had planned to do a Yurchenko 2½, which is 2 ½ twists in the air and one flip, but could only flip once, with no twists. Her low score for that vault ruined her chances for a medal. She left the competition in tears.

But Carey had one chance to bounce back at these Games, and took it.

In qualifying, Carey finished third on the floor exercise, behind Ferrari, who was first, and Simone Biles, in second. Biles elected not to compete in the final, though she announced Monday that she would participate in the balance beam final on Tuesday — her last possible event at the Tokyo Games.

Maggie Astor contributed reporting.