In the game of blackjack played with one​ deck,

Question

In the game of blackjack played with one deck, a player is initially 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

Given:

• There are 52 cards in the deck
• There are 4 aces
• There are 16 cards worth 10 points

Probability of getting an ace: 4/52

Probability of getting a card worth 10: 16/52

 

We realize that when we are given a second card, there are now only 51 cards in the deck. We will multiply 4/52 * 16/51 (because of the rules of multiplication, it doesn't matter which card is dealt first because 16/52 * 4/51 is equal).

 

4/42 * 16/51 = 64/2652 ≈ 0.024 or 2.4%