Question 478909: Dear Math teacher,
Could you help me please with the following problem?
Three cards are drawn from a pack of 52, each card being replaced before the next one is drawn. Compute the probability p that all are spades. A pack of 52 cards includes 13 spades.
Here is how I did it:
p = 13C3 / 52C3 = 286/22,100 = 0.0129 or 1.29%. However, this is NOT the right answer. My textbook's solution is solved like this: (13/52)^3 = 1/64 = 0.0156 or 1.56%.
Please let me know why my way does NOT give me the right answer.
Thank you so much as always.
Yours sincerely,
Ivanka
Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
Three cards are drawn from a pack of 52,
"each card being replaced before the next one is drawn"
P(all spades) = P(1st one a spade 'and' 2nd one a spade 'and' 3rd one a spade)
= 13/52*13/52*13/52 = 1/4*1/4*1/4 = 1/64 = .0156 OR 1.56%
"Without replacememt!"
P(all spades) = 13/52*12/51*11/50 = 1716/132,600 = 286/22,100 = .0129 OR 1.29%
What that says 'statistically' is that replacing the card...ups the chance of
all spades being drawn
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Three cards are drawn from a pack of 52, each card being replaced before the next one is drawn. Compute the probability p that all are spades. A pack of 52 cards includes 13 spades.
Here is how I did it:
p = 13C3 / 52C3 = 286/22,100 = 0.0129 or 1.29%.
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Comment: Your's is the probability of picking
a set of 3 clubs from all the sets of 3 cards.
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However, this is NOT the right answer. My textbook's solution is solved like this: (13/52)^3 = 1/64 = 0.0156 or 1.56%.
Comment: This is the probability of successively
selecting a club 3 times from a deck of 52 cards.
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Comment: An interesting difference.
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cheers,
Stan H.
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