Question

in the game of blackjack played with one deck, a player is intially dealt 2 different cards from the 52 different cards in the deck. A winning "blackjack" hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. The two cards can be in any order. Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?

Answer 1

Ans:- The total no of ways of dealing 2 cards from a deck of 52 cards = 52C2 = 52! / (50! * 2!) = 1326 ways

Now A blackjack consists of 1 of 4 aces and 1 of 16 other cards that are worth 10 points.

No of ways to select an ace :- 4 ways

No of ways to select a other card :- 16 ways

Total no of possible blackjacks = 4*16 = 64

Therefore, the probability of being dealt a blackjack hand = number of favourable outcomes/ Total outcomes

= 64/1326 = 0.04827

Approximately 4.827% of hands are winning blackjack hands