What are the chance three card from a deck of cards are all diamonds
The chance of drawing three cards from a deck of cards that are all diamonds can be calculated as follows:
There are 13 diamonds in a deck of 52 cards, so the probability of drawing the first diamond is 13/52.
After the first card is drawn, there are only 12 diamonds left in a deck of 51 cards, so the probability of drawing the second diamond is 12/51.
After the second card is drawn, there are only 11 diamonds left in a deck of 50 cards, so the probability of drawing the third diamond is 11/50.
Therefore, the probability that three cards drawn from a deck of cards are all diamonds is:
(13/52) x (12/51) x (11/50) = 0.00264105691 or about 0.26%.
To determine the chance of drawing three cards that are all diamonds from a standard deck of 52 cards, we need to calculate the probability.
Step 1: Determine the number of ways to draw three diamonds from a deck of 13 diamonds.
There are 13 diamonds in a deck, so we can choose 3 diamonds in C(13,3) ways.
Step 2: Determine the number of ways to draw three cards from the entire deck.
We can choose any 3 cards from a deck of 52 cards in C(52,3) ways.
Step 3: Calculate the probability.
The probability of drawing three cards that are all diamonds is the number of favorable outcomes divided by the number of possible outcomes.
Probability = C(13,3) / C(52,3)
C(n,r) represents the number of combinations when choosing r items from a set of n items.
Now, let's calculate the probability:
C(13,3) = (13!)/(3!(13-3)!) = 286
C(52,3) = (52!)/(3!(52-3)!) = 22,100
Probability = 286 / 22,100 = 0.01296 (rounded to 5 decimal places)
Therefore, the chance of drawing three cards that are all diamonds from a standard deck is approximately 0.01296 or 1.296%.