- #1
petha
- 1
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Hi, I am given the following problem.
Given the vector
x+a*y x,yin Zmq, a in Zq. 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*yi 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 (qm 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.
Given the vector
x+a*y x,yin Zmq, a in Zq. 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*yi 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 (qm 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.