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From a pack of 52 cards, two are drawn one by one without replacement. Find the probability that both of them are kings.

User Pcampr
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Final answer:

The probability of drawing two kings one by one without replacement from a 52-card deck is 1/221, found by multiplying the individual probabilities of drawing a king each time.

Step-by-step explanation:

To calculate the probability that both cards drawn from a standard deck of 52 cards are kings, we consider the probability of drawing a king both times without replacement. Initially, there are four kings in the deck of 52 cards, resulting in a probability of 4/52 for drawing a king on the first draw. Since one king has been drawn and is not replaced, there are now three kings left in a deck of 51 cards, giving a 3/51 probability of drawing a king on the second draw.

Now, to find the probability of both events occurring, we multiply the probabilities of each event:

  • Probability of first card being a king: 4/52
  • Probability of second card being a king after the first is drawn: 3/51

Thus, the probability that both drawn cards are kings is calculated as:

(4/52) × (3/51)

This results in 1/221 when simplified. Therefore, the probability of both cards being kings is 1/221.

User Arctic Pi
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