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?

ybarrap · Answer

4 aces
3 face cards per suit
1 10 card per suit
4 suits

ways to get blackjack: 1) face card and an ace
                                     =  (4choose1)*(3choose1)*(4choose1)
                                 2) 10 card and an ace
                                      =  (4choose1)*(4choose1)

3) total number of ways to deal a hand (52 choose 2)

P(blackjack)= (P(1) + P(2))/P(3)

= ((4choose1)^2(3choose1 + 1)/(52choose2)
 
= 4^2(3 + 1)/(52*51/2)

= 4^3/51/26

= .04827