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

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