Question

Four cards are dealt at random without replacement from an ordinary deck of 52 cards. If it is known that the four cards have different face values, what is the probability that the first two cards are spades

Answer 1

It is given that four cards are picked without replacement and these cards have different face values.

For the first draw, we have 52 cards, and we have to pick one suit. So, the probability for this is $\frac{13}{52}$.

For the second draw, only 51 cards are left. The second suit has to be selected, so there are 13 cards from that suit. The probability is $\frac{13}{51}$.

Similarly, the third and fourth draw have probabilities $\frac{13}{50}$ and $\frac{13}{49}$ respectively.

Since the draws are independent, the total probability becomes

$\frac{13}{52} * \frac{13}{51} * \frac{13}{50} * \frac{13}{49}$ = 0.004.

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Answer 2

Step-by-step explanation:

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