Three cards are drawn successively, without replacement from a back of 52 cards. Then, the
probability that the drawn cards are face cards of same suits, is
A standard deck of 52 playing cards consists of 4 suits: hearts, diamonds, clubs, and spades. Each suit has 3 face cards: the Jack, the Queen, and the King. That means there are a total of 12 face cards in the deck (3 face cards × 4 suits).
To find the probability that the three cards drawn are face cards of the same suit, we must calculate the probability that each card, drawn successively without replacement, is a face card of the same suit.
Let's assume we're looking for the probability that we draw three face cards all of the hearts suit (though the calculation applies to any suit).
1. The probability that the first card drawn is a face card of hearts is 3/52 since there are 3 face cards of hearts out of 52 cards total.
2. After drawing one face card of hearts, the deck now has 51 cards remaining, of which only 2 are face cards of hearts. The probability that the second card drawn is also a face card of hearts is now 2/51.
3. Finally, after drawing two face cards of hearts, the deck has 50 cards left, with just 1 remaining face card of hearts. The probability that the third card drawn is the remaining face card of hearts is 1/50.
The probability that all three cards drawn are face cards of the same suit is the product of these three probabilities:
P(3 face cards of the same suit) = (3/52) × (2/51) × (1/50)
Calculating this, we have:
P(3 face cards of the same suit) = (1/52) × (1/17) × (1/25) = 1/(52 × 17 × 25)
P(3 face cards of the same suit) = 1/22100
So, the probability that the three cards drawn are face cards of the same suit is 1/22100.