Two cards are dealt from a standard deck of 52 cards. What is the probability that the first card dealt is a $\diamondsuit$ and the second card dealt is a $\spadesuit$?
+23254 Since there are 13 diamonds and 52 cards, the probability that the first card is a diamond is 13/52.
Now, there are only 51 cards remaining and 13 of these cards are spades, so the probability that the second card is a spade is 13/51.
Combining these, the probability that the first card is a diamond AND the second card is a spade is:
13/52 x 12/51.
Multiply these together to get the final probability.
+33661 13 diamonds, so probability of 1st card being a diamond is 13/52 = 1/4
Given this, there are 51 cards left, 13 of which are spades, so probability that second card is now a spade = 13/51
Combined probability = (1/4)*(13/51) = 13/204 ≈ 0.064
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+23254 Since there are 13 diamonds and 52 cards, the probability that the first card is a diamond is 13/52.
Now, there are only 51 cards remaining and 13 of these cards are spades, so the probability that the second card is a spade is 13/51.
Combining these, the probability that the first card is a diamond AND the second card is a spade is:
13/52 x 12/51.
Multiply these together to get the final probability.
