What are the chances that a particular suit shows up at least once in the first two cards?

Question

A standard deck of 52 cards. It seems obvious that the probability of getting a particular suit (say diamonds) on the first try is 13/52. After that, if we do not get diamonds, our chances are 13/51. But how should we calculate the probability of getting at least once diamonds if we have two attempts?

Answer 1

Only read this after you've figured it out.

The number of trials that do not satisfy your condition is $\frac{39\cdot 38}{2}$: Select a non-$\diamondsuit$, then another one, and all you care about is, at the end, which suits you have, not the order in which they arrived, so divide by 2 to account for the same result occurring in two distinct ways.
Similarly, the number of total trials is $\frac{52\cdot 51}{2}$. You can use these to find the probability of failure, which easily leads to the probability of success.