6. Ten people are playing Black Jack (2 cards down for each). The dealer is using two decks. You will be the first to receive the first face up card. Your two down cards are a 2 and a 7. What is the probability that your face up card will be a face card (Jack, Queen, or King) ? Suppose it is not one of these, what is the probability that the next person's face up card will be a face card?

Step-by-step explanation:

There are two decks, so total number of cards = 52*2 = 104 cards

10 people are playing, 2 cards are down for each, so total 20 cards are down

your two cards are 2 & 7

now you receive the face up cars first

what is the probability that it is a face card

Total number of face cards = 3*4*2 = 24

total number of undistributed cards = 104 - 20 = 84

So probability = 24/84 = 2/7 = 0.2857

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Suppose if you got some other card, then in the deck still 24 facce cards are present and total number of ccards is reduced to 83

So Probability that next person's card is a face card = 24/83 = 0.2892