Answer to Question #8101 in Statistics and Probability for Neil Schliewe
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In fact this question is a little bit tricky.
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.
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?