Question

From a pack of 52 cards, two are drawn one by one without replacement. Find the probability that both of them are kings.

Answer 1

Consider the given events.
A = A king in the first draw
B = A king in the second draw

$$\begin{gathered} \mathrm{Now}, \\ P\left(A\right)=\frac{4}{52}=\frac{1}{13} \\ P\left(B/A\right)=\mathrm{Getting}\mathrm{a}\mathrm{king}\mathrm{in}\mathrm{the}\mathrm{second}\mathrm{draw}\mathrm{after}\mathrm{getting}\mathrm{a}\mathrm{king}\mathrm{in}\mathrm{the}\mathrm{first}\mathrm{draw} \\ =\frac{3}{51}\left[\mathrm{After}\mathrm{the}\mathrm{first}\mathrm{draw},\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{cards}\mathrm{will}\mathrm{be}51.\mathrm{Then},3\mathrm{kings}\mathrm{will}\mathrm{be}\mathrm{remaining}.\right] \\ =\frac{1}{17} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(A\cap B\right)=P\left(A\right)\times P\left(B/A\right)=\frac{1}{13}\times \frac{1}{17}=\frac{1}{221} \end{gathered}$$