Step-by-step explanation:
In a standard deck of 52 cards, face cards are cards with faces on them. There are 12 of them, 3 in each suit. They are also called “court cards,” because they show Kings, Queens and Jacks.” An Ace cannot be considered a “face card,” for the simple reason that it has no face on it.
a) Two cards are sevens, given there are no face cards
= ( 52- 12 face cards = 40)
= ( 4÷40×3÷40 = 0.1×0.075 = 0.0075 ( or) 0.75%
b. There is exactly one face card, given three of the cards are red
Total cards= (52-11 =41 cards)
assumed that the exactly one face card is not a red card
Red cards = (26-6 red face cards = 20 cards )
Picking Three red cards
=(20÷41 ×19÷40×18÷39 =0.487 ×0.475 ×0.461 =0.107 or 11%
c. Three cards are Aces, given one of the Aces was removed from the deck
Total cards = (52-1 ace card = 51 cards)
Picking three cards are ace
= (3÷51 ×2÷50×1÷49 = 0.059×0.04×0.02 = 0.0000472