Q62 / 200 · WBJEE 2013 · Mathematics

Cards are drawn one-by-one without replacement from a well shuffled pack of 52 cards. Then, the probability that a face card (jack, queen or king) will appear for the first time on the third turn is equal to

  • A
    $\frac{300}{2197}$
  • B
    $\frac{36}{85}$
  • Correct answer
    C
    $\frac{12}{85}$
  • D
    $\frac{4}{51}$

Solution

Ist turn Total number of face card $=12$ Total number of elements in sample space, $n(s)=52$ $\therefore P_{1}$ (no face card in first turn) $=\frac{52-12}{52}=\frac{40}{52}$ IInd turn $P_{2}$ (no face card in second turn) $$ =\frac{(52-13)}{(52-1)}=\frac{39}{51} $$ IIIrd turn $P_{3}$ (face card in third turn) $$ =\frac{(52-40)}{(51-1)}=\frac{12}{50} $$ $\therefore$ Required $P$ (face card on third turn) $$ \begin{array}{l} =P_{1} \times P_{2} \times P_{3} \\ =\frac{40}{52} \times \frac{39}{51} \times \frac{12}{50}=\frac{12}{85} \end{array} $$

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

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