Q78 / 160 · TS EAMCET 2018 (04 May Shift 2) · Mathematics

From a lot containing $n$ good and $m$ bad articles, if 2 articles are picked at random in succession without replacement, then the probability that the second article picked is bad is

  • Correct answer
    A
    $\frac{m}{m+n}$
  • B
    $\frac{m-1}{m+n}$
  • C
    $\frac{(n-1)(m-1)}{(m+n)^2}$
  • D
    $\frac{m n}{(m+n)^2}$

Solution

Good articles $=n$, bad articles $=m$ 2 articles are picked up without replacement $2^n$ is bad Conditions First bad and second bad or first Good and second bad $$ \begin{aligned} & \frac{m}{m+n} \cdot \frac{m-1}{m+n-1}+\frac{n}{m+n} \cdot \frac{m}{m+n-1} \\ & \frac{m^2-m+m n}{(m+n)(m+n-1)}=\frac{m(m+n-1)}{(m+n)(m+n-1)} \\ & =\frac{m}{m+n} \\ & \end{aligned} $$

Hence, the correct answer is option: 'A'.

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