Hi, I am given the following problem.(adsbygoogle = window.adsbygoogle || []).push({});

Given the vector

x+a*yx,yin Z^{m}_{q}, a in Z_{q}. What is the probability that there will be at least one zero in the sum?

My reasoning so far.

x+a*y= 0 either if a=0 or x_{i}= -a*y_{i}for some (or all) 1≤ i ≤ m

So by basic probability P(A U B) = P(A) + P(B) -P(A and B).

1 P(A) = P(a=0) = 1/q

2 P(B) = 1-P(No zeros) = 1 - ((q-1)/q)^{m}(q^{m}elements in total, (q-1)^{m}elements with no zeros.

P(A AND B) = P(A)*P(B) = 1/q(1-((q-1)/q)^{m})

So in total 1/q+1-((q-1)/q)^{m})-1/q*(1-(q-1)/q)^{m})

This looks like a total mess, but I am not certain what is wrong in my calculations.

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# A probability problem in Z_[q]

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