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14.Probability
medium
A man draws a card from a pack of $52$ playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is
A
$\frac{9}{{16}}$
B
$\frac{1}{{16}}$
C
$\frac{9}{{64}}$
D
None of these
Solution
(c) The required probability is given by
$= \frac{{{}^{39}{C_1}}}{{{}^{52}{C_1}}} \times \frac{{{}^{39}{C_1}}}{{{}^{52}{C_1}}} \times \frac{{{}^{13}{C_1}}}{{{}^{52}{C_1}}} $
$= \frac{3}{4} \times \frac{3}{4} \times \frac{1}{4} = \frac{9}{{64}}.$
Standard 11
Mathematics
