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?
- gôhpihánLv 71 decade agoFavorite Answer
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)
- Inquiry ComplexLv 41 decade ago
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
Adding them up: 48/52*4/51+4/52*3/51=1/13
- 1 decade ago
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
- 1 decade ago
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 helpsSource(s): my mathematical brain
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- buzLv 71 decade ago
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
- Anonymous1 decade ago
The way the question is posed, I understand this:
P(first is not a king, second is) + (OR) P(both are) = 48/52(4/51) + 4/52(3/51) = 0.076922 or, approximately, 0.08, 8%
- Andreas ALv 61 decade ago
4/52 * 3/51 = 0.0045