If you choose two cards at random from a deck of 52 cards, what is the probability that it is two diamonds?

A deck of cards contains 4 of each card (4 Aces, 4 Kings, 4 Queens, etc.)
Also there are 4 suits (Clubs, Hearts, Diamonds, and Spades).
Additionally, there are 13 cards in each suit (Clubs/Spades are black, Hearts/Diamonds are red) .

In this case, we are required to determine the probability of choosing two diamonds.

There are 13 diamonds in the deck.
Assuming, the cards were chosen without replacement;

P(Both cards are diamonds) = P(first card is diamond) × P(second card is diamond)

P(First card is diamond) = 13/52

If there was no replacement, then after picking the first diamond card, there are 12 diamond cards remaining and a total of 51 cards remaining in the deck.

Therefore;

P(Second card is diamond) = 12/51

Thus;

P(Both cards are diamonds) = 13/52 × 12/51

= 156/2652

= 1/17 or 0.0588

Hence, the probability of choosing two diamonds at random (without replacement) is 1/17 or 0.0588.