First card a spade, is the second a spade?

Question

You draw two cards one after another from a shuffled standard 52-card deck, without replacing the first. The first card is a spade. Given that, what is the probability the second card is also a spade?

Accepted Answer

A deck has 13 spades. After the first spade is removed, the deck holds: - 52 - 1 = 51 cards total, - 13 - 1 = 12 spades remaining. Since each remaining card is equally likely to come next: P(	ext{second spade} \mid 	ext{first spade}) = \frac{12}{51} = \frac{4}{17} \approx 0.235. Drawing one spade shrinks the spade pool from 13 to 12 and the deck from 52 to 51, so the second-spade chance dips just below the original 1/4. Takeaway. Condition by editing the deck: subtract the drawn spade from both the spade count and the total before evaluating the next draw.

First card a spade, is the second a spade?

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