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

0.02

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) )\\`

`=(1)/(51) (2)/(53) +(50)/(51) (1)/(53)`

`=(52)/(2703) \\=0.02`