A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Three cards are pulled in order from this deck of 52 playing cards. What is the probability that the cards will be three clubs?
follow the method I showed you in the previous post
To find the probability of drawing three clubs from a standard deck of 52 cards, you need to determine the number of favorable outcomes (drawing three clubs) and divide it by the total number of possible outcomes (drawing any three cards).
Step 1: Determine the number of favorable outcomes.
Since there are 13 clubs in a deck of 52 cards, the number of ways to choose 3 clubs from the 13 available is given by the combination formula, also known as "n choose k":
Combination of n choose k = n! / (k!(n-k)!)
In this case, n = 13 (the number of clubs) and k = 3 (the number of clubs drawn).
Combination of 13 choose 3:
C(13, 3) = 13! / (3!(13-3)!)
= 13! / (3! * 10!)
= (13*12*11) / (3*2*1)
= 286
Therefore, there are 286 ways to draw three clubs from the deck.
Step 2: Determine the total number of possible outcomes.
When drawing three cards from a deck of 52 cards, the total number of possible outcomes is given by the combination formula:
Combination of 52 choose 3:
C(52, 3) = 52! / (3!(52-3)!)
= 52! / (3! * 49!)
= 22,100
Therefore, there are 22,100 possible outcomes when drawing three cards from the deck.
Step 3: Calculate the probability.
To calculate the probability of drawing three clubs, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 286 / 22,100
≈ 0.0129
Therefore, the probability of drawing three clubs from a standard deck of 52 cards is approximately 0.0129 or 1.29%.
To find the probability of drawing three clubs, we first need to determine the total number of possible outcomes.
The total number of cards in the deck is 52. For the first card, since we want a club, there are 13 clubs out of the total 52 cards. Therefore, the probability of drawing a club on the first card is 13/52.
After drawing the first card, we have 51 cards left in the deck, including 12 clubs. So, for the second card, the probability of drawing a club is 12/51.
Now, after drawing the first and second cards, we have 50 cards left in the deck, including 11 clubs. Therefore, the probability of drawing a club on the third card is 11/50.
To find the probability of all three events occurring (drawing three clubs in order), we multiply the probabilities of each event:
(13/52) * (12/51) * (11/50) ≈ 0.048 or 4.8%
Therefore, the probability of drawing three clubs in order from a standard deck of cards is approximately 0.048 or 4.8%.