In a game of blackjack a 2card hand consisting of an ace and

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?

Solution

Chance of an ace in first card is 4/52. Chance of face card or 10 in 2nd card is 16/51 (only 51 since ace is now gone). Multiply answer by 2 since if order is reversed (face card then ace) this is also a black jack.

So 4/52 * 16/51 * 2 = 4.83%

For 2 decks chances are 8/104 and 32/103

So 8/104 * 32/103 * 2 = 4.78%