problema con recuento de registros

[Heimish2000]

Código SQL:

SELECT TIPO, SUM(PUB), SUM(PRI)
FROM
(
SELECT TIPO, CASE WHEN CARACTER = 'Público' THEN '1' ELSE '0' END AS PUB,
CASE WHEN CARACTER = 'Privado' THEN '1' ELSE '0' END AS PRI
FROM TIPOS
) AS MITABLA
GROUP BY TIPO