The question is suppose i have n balls out of which 1 has different weight(maybe higher of lower than other balls).Also i have been provided with k which is the number of weighings.Now i have to answer that after k weighings are over what is the minimum probability required to guess the fake ball(ball with different weight) for any general n and k?

fo eg : some example cases

n k min probability

3 1 0.500000

3 2 1.000000

4 1 0.500000

1 5 1.000000