On the one hand, it would seem that since the probability is the same for rain on each day, the chance he will return on day one two or three is 1/3 or .3333. On the other hand, since the probability of rain is given as 20%, it makes sense to say that by day three, the probability that he will head home each day is the same as the probability it will rain on that day. Where it gets complicated is when you start compounding probabilities that it will or won't rain on each day. For him to be headed home on day three, then it must not have rained on days one and two. The probability he heads home on day three is therefore the probability that it did NOT rain on day one, times the probability it did NOT rain on day two times the probability it DID RAIN on DAY three, or (.8 *.8*.2) or 12.8%. That's my guess and I'm sticking to it, so to all the mathematicians out there, please chime in! Is this right?
Bryant Michaels
MBA Admissions Consultant
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