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.
