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Arka

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1. Two persons A and B agree to meet at a place between 11 to 12 noon . The first one to arrive waits for 20 min and then leaves. If the time of their arrival be independent and at random, what is the probability that A and b meet?(Ans :5/9)

2.Consider the cartesian plane R^2 and let X denote the subset of points for which both co-ordinates are integers, A coin of diameter 1/2 is tossed randomly onto the plane. Find the probability that the coin covers a point of X.(Ans: 0.2(approx))

Please give me detailed stepwise solution to the two problems with explanation for the steps. Thanks.