If 3 cards are dealt from the standard deck, what is the probability of getting all cards the same suit?
Wrong yet again.
Since no suit is specified, the first card can be any of the 52 cards. The next two draws must be the same suit, so the probability of drawing 3 cards from the same suit is
52/52 * 12/51 * 11/50 = 22/425
I apologize for the incorrect response. You are correct.
The probability of drawing 3 cards from the same suit can be calculated as follows:
The first card can be any of the 52 cards, so the probability is 52/52.
The second card must be from the same suit, so there are 12 cards of the same suit remaining out of the remaining 51 cards. Thus, the probability is 12/51.
The third card must also be from the same suit, so there are 11 cards of the same suit remaining out of the remaining 50 cards. The probability is 11/50.
Therefore, the probability of drawing all 3 cards from the same suit is (52/52) * (12/51) * (11/50) = 22/425.
To find the probability of getting all cards the same suit when 3 cards are dealt from a standard deck, we need to determine how many favorable outcomes there are and divide it by the total number of possible outcomes.
Step 1: Determine the total number of favorable outcomes.
To have all three cards from the same suit, we need to choose a suit and then choose three cards from that suit. There are 4 suits to choose from, and once a suit is chosen, there are 13 cards in that suit to choose from. Therefore, the total number of favorable outcomes is 4 * (13 choose 3).
Step 2: Determine the total number of possible outcomes.
When 3 cards are dealt from a standard deck, there are (52 choose 3) possible outcomes, as we are choosing 3 cards from a deck of 52.
Step 3: Calculate the probability.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = (4 * (13 choose 3)) / (52 choose 3)
Now, we can simplify the expression and perform the necessary calculations to find the probability.
To find the probability of getting all cards the same suit, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
There are 4 suits in a standard deck: hearts, diamonds, clubs, and spades.
The number of favorable outcomes is when all 3 cards are from the same suit. Since there are 4 suits, the first card can be any suit, the second card must be the same suit as the first card, and the third card must also be the same suit. Therefore, there is only 1 favorable outcome.
The total number of possible outcomes is the total number of ways to choose 3 cards from a deck of 52. This can be calculated using the combination formula: C(52, 3) = 52! / (3!(52-3)!) = 22,100.
Therefore, the probability of getting all cards the same suit is 1 / 22,100, or approximately 0.000045.