If an 84 year old is diagnosed with cancer, what are the chances of him dying?

100%: Everyone dies, eventually. The chance that an individual dies of a particular kind of cancer vary with their overall health, the kind of cancer, where it is, and how widespread it is. Age reduces the patient's ability to recover, so the odds are worse that this cancer is what kills them, but i would need a lot more information to give a forecast of that sort, and even then i would have to guess.

Too many variables: It depends on the type of cancer, stage, other medical problems. Unfortunately this question cannot be answered without more details and then a rough estimate can be made.