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?
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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
| Is This Answer Correct ? | 3 Yes | 0 No |
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