Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a spade given that the second card is a club? (Round your answer to three decimal places.)

To find the probability that the first card is a spade given that the second card is a club, we can use conditional probability.

First, let's find the probability that the second card is a club.

A standard deck of 52 cards contains 13 clubs. So, the probability of drawing a club as the second card, without replacement, is 13/51.

Next, let's find the probability that the first card is a spade and the second card is a club.

There are 13 spades in the deck, so the probability of drawing a spade as the first card is 13/52.

Once the first card is drawn, there are 51 cards left in the deck, with 12 of them being clubs. So, the probability of drawing a club as the second card, given that the first card is a spade, is 12/51.

Finally, we can find the probability that the first card is a spade given that the second card is a club by using conditional probability formula:

P(A|B) = P(A and B) / P(B)

P(spade|club) = P(spade and club) / P(club)

P(spade|club) = (13/52 * 12/51) / (13/51)

Simplifying, we get:

P(spade|club) = 12/52 = 3/13

Therefore, the probability that the first card is a spade given that the second card is a club is 3/13, which is approximately 0.231 when rounded to three decimal places.

There are 13 spades in a deck of cards.

You know the suit of the second card, so the suit of 51 cards is unknown.

The probability is 13/51