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Q.

One card is missing from a normal pack of 52 playing cards. A card is drawn from the remaining pack of cards. If a spade card is obtained then the chance of getting a spade card by drawing another card from remaining 50 cards is____

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a

$\frac{1}{17}$

b

$\frac{2}{17}$

c

$\frac{4}{17}$

d

$\frac{3}{17}$

answer is D.

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Detailed Solution

$E_{1}$ denotes getting spade in first draw, $E_{2}$ denotes getting spade in second draw
$P (E_{1}) = \frac{1}{4} \times \frac{12}{51} + \frac{3}{4} \times \frac{13}{51} = \frac{1}{4} P (E_{1} \cap E_{2}) = \frac{1}{4} \times \frac{12}{51} \times \frac{11}{50} + \frac{3}{4} \times \frac{13}{51} \times \frac{12}{50} = \frac{1}{17} P (\frac{E_{2}}{E_{1}}) = \frac{P (E_{1} \cap E_{2})}{P (E_{1})} = \frac{4}{17}$

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