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Three cards are drawn randomly successively without replacement from a pack of 52 shuffle cards. What is the probability that the drawn cards are face cards of the same suit?

a) 1/416
b) 1/221
c) 1/17
d) 1/68

User Chrisan
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Final answer:

The probability of drawing three face cards of the same suit from a deck without replacement is 1/22100, which simplifies to 1/221. The correct answer is option b).

Step-by-step explanation:

The probability of drawing three face cards of the same suit without replacement from a standard deck of 52 cards can be calculated by multiplying the probabilities of each event: Multiplying these probabilities gives us:(3/52) * (2/51) * (1/50) = 1/22100Now, we simplify this fraction to get the simplest form:1/22100 can be simplified to 1/17 * 1/1300, and further to 1/221. Therefore, the correct answer is 1/221, which corresponds to option b).

The probability that the second card drawn is a face card of the same suit as the first card (there are 3 face cards of the same suit as the first card out of 51 remaining cards in the deck).Finally, the probability that the third card drawn is a face card of the same suit as the first two cards can be calculated in a similar way. We multiply these probabilities to obtain the overall probability:P(face cards of same suit) = (12/52) * (3/51) * (2/50) = 1/221

User Shantha Kumara
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