Three cards are randomly selected, one at a time (without return), from a standard deck of 52 cards. What is the probability that the last two of the three cards are spades? (Answer in lowest terms).
Choose the correct answer: A) 18/750 B) 19/750 C) 18/850 D) 39/850 E) 39/750
A standard deck has 52 cards of which 13/52 are spades, so the probability of not getting a spade is P(NS) = (52-13)/4 on the first selected card.   Because selection is (without return), the P(S) has changed for following selections. Now, there are 51 cards and number spades is dependent upon whether first card was a spade, or not... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is:   Formula = P(A\B) = P(A and B)/P(B).   P(A\B) = (39/52)(13/51)(12/50) = 6084/132600 = 39/850   Answer: 39/850
<result>D</result>
Three cards are randomly selected, one at a time (without return), from a standard deck of 52 cards. What is the probability that the last two of the three cards are spades? (Answer in lowest terms).