SOLUTION: If three cards are removed at random, one at a time without replacement, find the probability that at least one of the cards is a face card.

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Question 414314: If three cards are removed at random, one at a time without replacement, find the probability that at least one of the cards is a face card.
Found 2 solutions by sudhanshu_kmr, ewatrrr:
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

no. of face cards = 12 , nonface card = 40
probability that all cards are non-face cards P(A) = 40C3 / 52C3
= 9880/22100
= 0.447

probability that at least one cards is a face card = P'(A) = 1-P(A) = 0.552

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

three cards removed at random, one at a time 'without replacement'

Given there are 12 face cards(jack, queen,king in each the 4 suits)

 40 of the cards are 'not' face cards

P(at least one of the cards is a face card) = 1 - P(no face cards) 

 1 - P(no face cards) = 1 - 40/52*39/51*38*50



Note: w/o replaceement: 

the number of non-face cards and the number of cards is one less when next card is drawn