# if two cards are drawn from a well shuffled pack , then the probability that atleast one of the two is heart is

Please find below the solution to the asked query:

$\mathrm{Number}\mathrm{of}\mathrm{ways}{=}^{52}{\mathrm{C}}_{2}\phantom{\rule{0ex}{0ex}}\mathrm{Required}\mathrm{ways}=\phantom{\rule{0ex}{0ex}}\frac{\mathrm{Select}\mathrm{one}\mathrm{heart}\mathrm{AND}\hspace{0.17em}\mathrm{One}\mathrm{non}-\mathrm{heart}+\mathrm{Select}\mathrm{both}\mathrm{heart}}{{}^{52}{\mathrm{C}}_{2}}\phantom{\rule{0ex}{0ex}}=\frac{{}^{13}{\mathrm{C}}_{1}{\times}^{39}{\mathrm{C}}_{1}{+}^{13}{\mathrm{C}}_{2}}{{}^{52}{\mathrm{C}}_{2}}\phantom{\rule{0ex}{0ex}}=\frac{507+78}{1326}\phantom{\rule{0ex}{0ex}}=\frac{585}{1326}\phantom{\rule{0ex}{0ex}}=\frac{195}{442}$

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