Write SQL query to solve given problem: What is the percentage of female athletes below 20s who participated in the 2002 Winter Olympic?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT CAST(COUNT(CASE WHEN T3.gender = 'F' THEN 1 ELSE NULL END) AS REAL) * 100 / COUNT(T2.person_id) FROM games AS T1 INNER JOIN games_competitor AS T2 ON T1.id = T2.games_id INNER JOIN person AS T3 ON T2.person_id = T3.id WHERE T1.games_name = '2002 Winter' AND T2.age < 20