A standard deck of 52 cards contains four suit: hearts,diamonds, clubs and spades. Each suit has 13 cards: ace, 2,3,4,5,6,7 8,9,10, Jack queen, and king. Two cards are randomly drawn without replacement. Calculate the probability of drawing two diamond cards.
There are 13 diamond cards in the deck, so the probability of drawing a diamond on the first draw is 13/52. After the first card is drawn, there are 12 diamond cards left in the deck out of 51 total cards remaining. Therefore, the probability of drawing another diamond on the second draw, given that the first card was a diamond, is 12/51.
To calculate the probability of both events happening (drawing two diamond cards), we multiply the probabilities:
(13/52) * (12/51) = 3/52
So the probability of drawing two diamond cards from a standard deck of 52 cards is 3/52, or approximately 0.0588, or about 5.88%.
To calculate the probability of drawing two diamond cards, we need to consider the number of favorable outcomes and the total number of possible outcomes.
1. Number of favorable outcomes:
The first card drawn can be any of the 13 diamond cards. Once that card is drawn, there are 12 diamond cards remaining for the second draw. Therefore, the number of favorable outcomes is 13 * 12 = 156.
2. Total number of possible outcomes:
The first card can be any of the 52 cards in the deck. Once that card is drawn, there are 51 cards remaining for the second draw. Therefore, the total number of possible outcomes is 52 * 51 = 2652.
3. Probability of drawing two diamond cards:
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 156 / 2652
Probability ≈ 0.0588 or 5.88%
Therefore, the probability of drawing two diamond cards is approximately 0.0588 or 5.88%.