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I am assuming that since the question asks if he will leave on Monday, we're not worried about Sat. or Sun. and thus there is an 80% chance he will not go home Sat., 80% chance he will not go home on Sun., and a 20% he will leave on Monday.
because it's the probability that he would "leave" on monday and not that he would "stay" on monday. Therefore, you have to take into account the probability on the 3rd day that it is raining (20%), so that he would leave on that day