Question

From a deck of cards, three cards are drawn on by one without replacement. Find the probability that each time it is a card of spade.

Answer 1

Consider the events
A = An ace in the first draw
B = An ace in the second draw
C = Getting an ace in the third draw

$$\begin{gathered} \mathrm{Now}, \\ P\left(A\right)=\frac{13}{52}=\frac{1}{4} \\ P\left(B/A\right)=\frac{12}{51}=\frac{4}{17} \\ P\left(C/A\cap B\right)=\frac{11}{50} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(A\cap B\cap C\right) \\ =P\left(A\right)\times P\left(B/A\right)\times P\left(C/A\cap B\right) \\ =\frac{1}{4}\times \frac{4}{17}\times \frac{11}{50} \\ =\frac{11}{850} \end{gathered}$$