When playing the card game Blackjack, multiple decks are used and reshuffled often so that the outcomes of the cards dealt are approximately independent. When a player receives two cards that are a combination of an ace and a face card, this is called a "natural blackjack" and automatically wins. A natural blackjack should occur in 4.5% of the rounds played. What is the probability that a player plays 20 rounds of Blackjack and gets two or more natural blackjacks?

Question

Advanced Placement (AP)

Whiskers

9 January, 19:24

When playing the card game Blackjack, multiple decks are used and reshuffled often so that the outcomes of the cards dealt are approximately independent. When a player receives two cards that are a combination of an ace and a face card, this is called a "natural blackjack" and automatically wins. A natural blackjack should occur in 4.5% of the rounds played. What is the probability that a player plays 20 rounds of Blackjack and gets two or more natural blackjacks?

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Cameron · Answer 1

The correct answer is (C) or. 227. The number of natural blackjacks (X) follows a binomial distribution with n=20, p=0.045.

Explanation:

P (X≥2) = 1-P (X≤1) = 1-0.773=0.227.