Quote:
Originally Posted by Phloston
The correct answer is B. The fact that the patient survived to one year is irrelevant, as would if he had survived two or three. Choice B represents the probability of surviving all four years.
This is not the same as asking the probability of landing three additional tails (1/8) if a previous one has already been landed. That's the logic that choice D would follow.
Choice B would be analogous to asking what's the probability of landing four tails in a row. This is independent of whether one, two or three have already been landed. The question's just asking how likely it is that this patient will live four years.
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Don't think this reasoning is correct. Take the tails example. If the patient had died the first year, (i.e. heads), he'd have a 0% of making it to 4/4 years. If he lived (i.e. rolled tails), his probability of reaching 4 tails in a row would now rely solely on the last 3 spins (i.e. .5 x .5 x .5 = 1/8).
I actually looked this up online after doing the offline version of this morning. Most boards online say the answer is D and that the answer key is just incorrect. This happens a lot with bootlegged versions of these exams.