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Answer to Question #8101 in Statistics and Probability for Neil Schliewe

Question #8101
If 2 cards are drawn from a normal deck of 52 cards, what is the probability that both cards will be spades?
Expert's answer
There 1/4*52 spades in the deck.Probability to pick a spade taking single card is 1/4. Due to multiplication rule probability to pick two cards-spades is 1/4*1/4=1/16

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Assignment Expert
03.04.12, 15:21

In fact this question is a little bit tricky.

If we
consider drawing one card, putting it back in the deck, regardless if it
is a spade or not, then reshuffling the deck and drawing the second
card, the probability is 1/4 x 1/4 =1/16 This is the same as 1/4 x 1/4 = 1/16.Or we can consider experiment as picking two cards at a time. For each of them probability to turn out spade is 1/4.

On the other hand, if we draw firstly one card& it is spade with probability 1/4. If a second card drawn, there's one less spade in the deck, so the
probability on the second draw is 12/51.

The probability of
drawing two spades from a deck is 0.25 x 12/51 = 0.058824 This is called
sampling without replacement. In quality control, it is very common to
sample without replacement as bad parts are discarded.

Neil Schliewe
03.04.12, 15:12

Don't you have to account for the fact that this is a dependent event? Taking 2 cards the second card should be only 12/51 - correct?

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