91Ó°ÊÓ

A deck of cards is well-shuffled and then divided into two halves of 26 cards each.

A card is drawn from one of the halves; it turns out to be an ace and it placed in the second half

The half is then shuffled, and a card is drawn from it.

We have to find the probability that this drawn card is an ace.

Let$E=\{$the first card drawn is an Ace$\}$

$F=\{$The second card drawn is the original Ace drawn in the first round$\}$$G=\{$the Second card drawn is an Ace $\}$

The number of cards in the second half after an ace is placed is 27.

The conditional probability of getting an ace given that interchanged card is selected is,$P(Fâˆ\pounds E)=\frac{1}{27}$

The conditional probability of getting an ace given that interchanged ace card is not selected is$P\left(F^câˆ\pounds E\right)=1-P(Fâˆ\pounds E)$

$=1-\frac{1}{27}$

$=\frac{26}{27}$

The probability of getting an ace out of the remaining 51 cards pack is,
$P\left(Gâˆ\pounds F^{*}âˆ\copyright E\right)$$=\frac{3}{51}$