Answer / guest

52 / 2703

There are two cases to be considered.

CASE 1 : King of Hearts is drawn from Pack A and shuffled
with Pack B

Probability of drawing King of Hearts from Pack A = 1/51
(as Queen of Hearts is not to be drawn)
Probability of having King of Hearts on the top of the Pack
B = 2/53

So total probability of case 1 = (1/51) * (2/53) = 2 / (51
* 53)

CASE 2 : King of Hearts is not drawn from Pack A

Probability of not drawing King of Hearts from Pack A =
50/51 (as Queen of Hearts is not to be drawn)
Probability of having King of Hearts on the top of the Pack
B = 1/53

So total probability of case 2 = (50/51) * (1/53) = 50 /
(51 * 53)

Now adding both the probability, the required probability
is
= 2 / (51 * 53) + 50 / (51 * 53)
= 52 / (51 * 53)
= 52 / 2703
= 0.0192378

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