Two identical pack of cards A and B are shuffled throughly. One card is picked from A and shuffled with B. The top card from pack A is turned up.
If this is the Queen of Hearts, what are the chances that the top card in B will be the King of Hearts?
At the outset, it is observed that the given problem admits of the following two cases:
CASE 1: King of Hearts is NOT drawn from Pack-A
We know, that the Queen of Hearts is NOT to be drawn.
Accordingly, it follows that the probability of NOT drawing King of Hearts from Pack -A = 50/51, and:
The probability that the King of Hearts is located at the top of Pack-B=1/53 Consequently, the total probability corresponding to CASE 1
= (50/51)*(1/53) = 50/(51*53)
CASE 2: King of Hearts is drawn from Pack-A and then shuffled with Pack-B
We note that Queen of Hearts is NOT to be drawn.
Accordingly , the probability of drawingHzKing of Hearts from PACK-A=1/51
Also, the probability that King of Hearts is located on top of PACK-B =2/53
Therefore, the probability for CASE 2:
= (1/51)*(2/53) = 2/(51*53)
Consequently , the required probability
=Prob (CASE 1) + Prob(CASE 2)
= 50/(51*53)+ 2/(51*53)
= 52/2703
=0.01923788383...
Edited on December 31, 2021, 6:30 am
Puzzle Solution
