Question

Two cards are drawn together from a pack of 52 cards the probability one is spade and one is heart is?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{S}\mathrm{be}\mathrm{the}\mathrm{sample}\mathrm{space} \\ \mathrm{Then},\mathrm{n}\left(\mathrm{S}\right){=}^{52}{\mathrm{C}}_2=\frac{\left(52\times 51\right)}{2\times 1}=1326 \\ \mathrm{Let}\mathrm{E}=\mathrm{event}\mathrm{of}\mathrm{getting}1\mathrm{spade}\mathrm{and}1\mathrm{heart} \\ \therefore \mathrm{n}\left(\mathrm{E}\right)=\mathrm{number}\mathrm{of}\mathrm{ways}\mathrm{of}\mathrm{choosing}1\mathrm{spade}\mathrm{out}\mathrm{of}13\mathrm{and}1\mathrm{heart}\mathrm{out}\mathrm{of}13 \\ {=}^{13}{\mathrm{C}}_1{\times }^{13}{\mathrm{C}}_1 \\ =13\times 13 \\ =169 \\ \therefore \mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{169}{1326}=\frac{13}{102} \end{gathered}$$

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