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Hospital or else. Only IW that know why he survived but maybe he's survive because his wound is not heavy.

EDIT: Explosions have random outcomes. When the tanker exploded, it could have been more devastating to SSG. Griggs than it was to Sgt. MacTavish.

Also, it is possible that Captain Price survived, as well. Infinity Ward has said he survived in a magazine article. (I have no reference, so consider it just, "possible," that he survived)