Question

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

Answer 1

Answer:

1/17 or 0.0588 (without replacement)

Step-by-step explanation:

To answer this question we need to know the following about a deck of cards

• 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.