Three cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. (Round your answer to four decimal places.)
Three cards of the same suit are drawn
13 cards in each suit.
1st card has to be some suit.
Given that,
P(same,same) = 12/51 * 11/50
what is answer
To find the probability of drawing three cards of the same suit, we need to consider the number of favorable outcomes (drawing three cards of the same suit) and the total number of possible outcomes (drawing any three cards).
First, we can determine the number of favorable outcomes. There are four suits in a deck of cards (hearts, diamonds, clubs, and spades). If we want to draw three cards of the same suit, we can choose any of the four suits. Once we have chosen a suit, we need to select three cards from that suit. There are 13 cards of each suit (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King), so we can choose three cards from this set of 13 cards. Therefore, the number of favorable outcomes is:
4 (suits) * 13C3 (choosing three cards from the selected suit)
Next, we can determine the total number of possible outcomes. Since we are drawing three cards without replacement, the first card can be any of the 52 cards in the deck. After that, there are 51 cards remaining, and the second card can be any of these 51 cards. Finally, for the third card, there are 50 cards remaining. Therefore, the total number of possible outcomes is:
52C1 (choosing the first card) * 51C1 (choosing the second card) * 50C1 (choosing the third card)
Now, we can calculate the probability 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 = (4 * 13C3) / (52C1 * 51C1 * 50C1)
Calculating this expression will give us the probability of drawing three cards of the same suit. The result should be rounded to four decimal places.
To find the probability of drawing three cards of the same suit, we first need to determine the total number of ways to choose three cards from a deck of 52 cards without replacement.
The total number of ways to choose 3 cards from a deck of 52 cards without replacement can be calculated using the concept of combinations. The formula for combinations is:
nCr = n! / (r!(n - r)!)
Where n represents the total number of items and r represents the number of items selected.
Using this formula, the total number of ways to choose 3 cards from a deck of 52 cards is:
52C3 = 52! / (3!(52 - 3)!)
Now, to find the probability of drawing three cards of the same suit, we need to determine the number of favorable outcomes.
In a deck of 52 cards, there are four suits (hearts, diamonds, clubs, spades), and each suit contains 13 cards. Therefore, we have 13 cards of the same suit.
To calculate the number of favorable outcomes, we need to choose any one of the four suits (since every suit has the same number of cards) and then choose 3 cards from that suit.
The number of ways to choose 3 cards from a suit with 13 cards without replacement can be calculated as:
13C3 = 13! / (3!(13 - 3)!)
Since there are four suits, we multiply this by 4 to get the total number of favorable outcomes.
Number of favorable outcomes = 4 * (13C3)
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= (4 * (13C3)) / (52C3)
Final step, calculate the probability by evaluating the above expression:
Probability = (4 * (13! / (3!(13 - 3)!))) / (52! / (3!(52 - 3)!))
Simplifying this expression will give us the probability of drawing three cards of the same suit.