Multiple choice

A Urn contains 'm' white and 'n' black balls. Balls are drawn one by one till all the balls are drawn. Probability that the second drawn ball is white, is

  1. $\displaystyle \frac {m}{m+n}$
  2. $\displaystyle \frac {m(n-1)}{(m+n)(m+n-1)}$
  3. $\displaystyle \frac {m(m-1)}{(m+n)(m+n-1)}$
  4. $\displaystyle \frac {mn}{(m+n)(m+n-1)}$
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A Correct answer
Explanation

By symmetry, the probability of any specific ball being drawn at any specific position (without knowing the outcomes of other draws) is equal to the initial proportion of that ball in the urn. Since there are m white balls out of m+n total balls, the probability that the second ball is white is m/(m+n).

AI explanation

By symmetry, any ball in the urn has an equal probability of being the second one drawn. The probability that the second drawn ball is white is therefore identical to the probability that the very first ball drawn is white. Since there are m white balls out of a total of m+n balls, the probability is m/(m+n). The result is m/(m+n).

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