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Can insecure algorithms be combined to form a secure algorithm?

This is hypothetical as I can't think of any reason to do this, but out of curiosity..

Could I, for example, take the MD5 digest of a message and concatenate it with the SHA-1 digest (not quite broken, but getting close), to form a secure concatenated digest? Intuitively, I would think the chances of finding a collision that crossed the two algorithms would be low enough to make this secure, but I'm not sure how to verify that.