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In the game of blackjack, the picture cards (jack, queen, king) count as 10 points and the ace counts as either 1 or 11 points. All other cards are counted at their face value. Blackjack is achieved if 2 cards total 21 points. What is the probability of getting blackjack in this problem?

Options:
a. 0.0583
b. 0.0483
c. 0.0383
d. 0.0283

User Borrible
by
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1 Answer

2 votes

Final answer:

The probability of getting a blackjack is calculated by dividing the number of blackjack combinations by the total number of possible two-card combinations. The result is a probability of 0.0483.

Step-by-step explanation:

The question asks about calculating the probability of achieving a blackjack in the game. A blackjack occurs when the two cards dealt add up to 21 points. Given that we have 52 cards in a deck, we can calculate this probability by considering all the combinations that would result in a total of 21. There are four aces in the deck and sixteen cards (four 10s, four Jacks, four Queens, and four Kings) that count as 10 points. We can form a blackjack by drawing an ace and a ten-point card. Since we can have any combination of the ace from any suit and the ten-point card from any suit, we have 4 aces × 16 ten-point cards = 64 blackjack combinations.

To find the probability, we divide the number of blackjack combinations by the total number of two-card combinations possible. The number of two-card combinations from a 52-card deck is given by the formula for combinations: C(52, 2) = 52! / (2! × (52 - 2)!) = 1326. Therefore, the probability of getting a blackjack is 64 / 1326 which simplifies to 0.0483 or 4.83%.

The correct answer to the student's question is option b: 0.0483.

User Donald Jansen
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