Question

Q3. Consider two identical pack of cards A and B. When one card from A is taken and shuffled with the card B, the first top card of A is the Queen of hearts. What will be the probability that the top card of B to be King of hearts

Answer 1

Answer:

0.02

Step-by-step explanation:

Pack A and B both consisted of 52 cards. When shuffled, 51 cards in A and 53 cards in deck B. It appears that the Top card of A left with only 51 possible cards to be taken from A (since we know the Queen hadn't moved).

The two possible cases are: probability of not taking King of Hearts (from A to B), and the other were we did.

Let K= the event of taking the King of Hearts from A to B and be $B_{K}$ the occasion being the top card of B.

$P(B_{K} )=P(K)P(B_{K} |K)+P(K^{C} )P(B_{K} |K^{C} )$

$=\frac{1}{51} \frac{2}{53} +\frac{50}{51} \frac{1}{53}$

$=\frac{52}{2703} \\=0.02$