Two cards are drawn one by one without replacement from a well shuffled pack of 52 cards. What is the probability that one of the cards drawn is a king and the other a queen of the same suit?

Solution

Let A and B denote the two events
$straight P left parenthesis straight A right parenthesis space equals space straight P left parenthesis ace right parenthesis space equals space 4 over 52 comma space space straight P left parenthesis straight B right parenthesis space equals space straight P left parenthesis queen space of space the space same space suit space as space that space of space ace right parenthesis space equals space 1 over 51$
Required probability = $4 over 52 cross times 1 over 51 space equals 1 over 663$

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Probability

Two cards are drawn one by one without replacement from a well shuffled pack of 52 cards. What is the probability that one of the cards drawn is a king and the other a queen of the same suit?

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