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

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Number} \mathrm{of} \mathrm{ways}{=}^{52}{\mathrm{C}}_2 \\ \mathrm{Required} \mathrm{ways}= \\ \frac{\mathrm{Select} \mathrm{one} \mathrm{heart} \mathrm{AND}\hspace{0.17em}\mathrm{One} \mathrm{non}-\mathrm{heart}+\mathrm{Select} \mathrm{both} \mathrm{heart}}{{ }^{52}{\mathrm{C}}_2} \\ =\frac{{ }^{13}{\mathrm{C}}_1{\times }^{39}{\mathrm{C}}_1{+}^{13}{\mathrm{C}}_2}{{ }^{52}{\mathrm{C}}_2} \\ =\frac{507+78}{1326} \\ =\frac{585}{1326} \\ =\frac{195}{442} \end{gathered}$$

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