In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (Round your answers to four decimal places.)
(a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?
(b) If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?

Question

In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (Round your answers to four decimal places.)
(a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack? 
(b) If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?

anonymous · Answer

a) the winning hands are ace + facecard or facecard + ace, so the probability of getting an ace in the first card is 4/52 (there are four aces) and then a facecard or ten is 16/52, so for ace + facecard or 10 you have 4/52 * 16/51 = 64/2652 probability, for facecard + ace it's the same, so the probability of a blackjack is 128/2652 = 0.048

anonymous · Answer

b) The same way:
ace + facecard or 10: 
8/104 for ace
32/103 for facecards and ten

For blackjack:

8/104 * 32/103 * 2 = 0.047