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-adjaent pu 6. A neighbourhood consists of 132 households. Of these 65 subscribe for newpaper (bp) A, 45-for paper B and 42 for paper C. It is also the case that 20 of the households subscribe for both A and B, 25 for A and C, 15 -for B and C, as well as 8 households subscribe for all three. Find the probability that a random household from the neighbourhood 132 (a) subscribes solely for newspaper A; (b) subscribes for none of these. 7. Find the probability that the difference in squares 2 -y2 of two random integers z, y is divisible by 3. ( (Hint: An integer is divisible by 3 iff the remainder of division by 3 is 0. Observe that -y? and (r+3t)-(u+36) are both divisible by 3 at the same time, no matter s,t e Z. Thus, to build the sample space, it suffices to consider the function /(z,U)-|2,2-v2]3-2-v2 mod 3 for x, y E Z3 = {1013, [113,1213), ie, mod 3)

Answer 1