- #1

petha

- 1

- 0

Given the vector

**x**+a*

**y**

**x**,

**y**in 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.