Question

Two cards are drawn from a deck of 52 cards. What is the probability that 2 cards drawn are either aces or black cards?

Answer 1

$$\begin{gathered} \because \mathrm{P}(2\mathrm{aces})=\frac{4}{52}\times \frac{3}{51}=\frac{12}{52\times 51}, \\ \mathrm{P}(2\mathrm{black}\mathrm{cards})=\frac{26}{52}\times \frac{25}{51}=\frac{26\times 25}{52\times 51} \\ \mathrm{and},\mathrm{P}(2\mathrm{black}\mathrm{aces})=\frac{2}{52}\times \frac{1}{51}=\frac{2}{52\times 51} \\ \therefore \mathrm{P}(\mathrm{either}\mathrm{aces}\mathrm{or}\mathrm{black}\mathrm{cards})=\mathrm{P}(2\mathrm{aces})+\mathrm{P}(2\mathrm{black}\mathrm{cards})-\mathrm{P}(2\mathrm{black}\mathrm{aces}) \\ =\frac{12}{52\times 51}+\frac{26\times 25}{52\times 51}-\frac{2}{52\times 51} \\ =\frac{662-2}{52\times 51} \\ =\frac{660}{52\times 51} \\ =\frac{55}{13\times 17} \\ =\frac{55}{221} \end{gathered}$$