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?
Well since you know the Queen of Hearts is in the A deck this means that there is a 1/51 chance that the card moved from the A to the B deck was the king of hearts. So in order to find the probability of the card on the top being a king of hearts you would have to do a weighted average. probability of drawing a king of hearts in the B deck=1/51(2/53)+50/51(1/53)=.019238 or 1.9238%. Basically what all these numbers mean is, there is a 1 out of 51 chance the king of hearts will go into the B deck giving you a 2 out of 53 chance of drawing the king of hearts, and 50 out of 51 times the king of hearts will not go into the B deck giving you a 1/53 chance of drawing a king of hearts in the B deck.
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