Question

Three cards are drawn successively, without replacement from a pack of $52$ well shuffled cards. What is the probability that first two cards are kings and third card drawn is an ace?

Answer 1

Consider the given events.

In a pack of $52$ well shuffled cards
$A=$ A king in the first draw
$B=$ A king in the second draw
$C=$ An ace in the third draw

Probability of an event $=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$
Now,

$P\left(A\right)=\frac{4}{52}=\frac{1}{13}$ [Since, $K=4,n=52$]

$P\left(B/A\right)=\frac{3}{51}=\frac{1}{17}$ [Since, $K=3,n=51$]

$P(C/A\cap B)=\frac{4}{50}=\frac{2}{25}$ [Since, $A=4,n=50$]

Hence. the required probability,

$=P\left(A\right)\times P\left(B/A\right)\times P(C/A\cap B)$

$=\frac{1}{13}\times \frac{1}{17}\times \frac{2}{25}$

$=\frac{2}{5525}$