A random Algorithm $A$ receives input in $[n]$ it's know that when the probability is taken over input that was chosen randomly over uni-formal distribution over the algorithm randomness the probability $A$ succeeds is at least $2/3$. Prove that if we randomly pick $k \in [n]$ then with probability of at least $1/3$ we shall get such k such that the algorithm succeeds with probability of at least $1/2$ Any help\directions would be great
random Algorithm over Random input-help needed
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probability
algorithms
probability-theory
probability-distributions