Matching Ranks

Condition on the first card and ask about the second.

After the first card, how many of the remaining 51 cards match its rank?

1. 1. Condition on first card

   The first card can be anything; 3 of the remaining 51 cards share its rank.

2. 2. Compute probability

   Probability the second card matches is $3/51=1/17$.

   $$P=\frac{3}{51}=\frac{1}{17}$$

Answer: 1/17