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# Two cards are drawn out of a 52 card deck without replacement. what is the probability ..?

Two cards are drawn out of a 52 card deck without replacement. What is the probability that the second card is a king?

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you don't need to know the first card, after we drawn the first card, there will be 51 cards left, and there are 4 kings (diamond, club, hearts, spade)

there is 2 situations,

1st situation is that you draw a card that isn't a king, then draw a king

2nd situation is that you draw both cards that are king

48/52 * 4/51= 16/221 (1st situation)

4/52 * 3/51 = 1/221 (2nd sitiation)

total probability is:

16/221 + 1/221= 17/221 or 7.69%

(this only applies for the 52 card deck to have all different cards and 4 types of flower for each card)

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• Case 1: The first card is not a king.

Chance for this is occur and the second card being a king is 48/52*4/51.

Case 2: The first king is a king.

Chance for this to occur and the second card being a king is 4/52*3/51

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• First the probability that the first one is king is 4/52, the probability of the second being king again is 3/51. So the chance of getting two kings is (4/52)*(3/51) Prob.1

Second the probability of not getting a king on the first and king on the second is (48/52)*(4/51)... Prob. 2

So if you are only interested on the probability of getting a king on the second draw neglecting the first draw, just add the two probabilities..Prob.1+Prob.2

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• the answer given is incorrect as we do now know the first card.

P(second card is a king)=P(first card is a king and the second is too) or P(first card isnt a king but the second is)

P(first card is a king and so is the second one) = 4/52 * 3/51 = 1/221

P(first card isnt a king and second one is) = 48/52 * 4/51 = 16/221

so the overall probability is

P(first card is a king and the secon one)+P(first card isnt and the second is) = 1/221 +16/221= 17/221 = 0.0769....

THE EXAMPLE ABOVE IS WRONG!! this is correct. hope it helps

Source(s): my mathematical brain
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• i'd say its:

4/52 * 3/51 = .004525 (if the first card is a king) PLUS

48/52 * 4/51 = .072398 (if the first card isn't a king)

for a total of .076923

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• Anonymous
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