Questions: Paul went to a blackjack table at the casino. At the table, the dealer has Just shuffled a standard deck of 52 cards. Paul has had good luck at blackjack in the past, and he actually got three blackjacks with Kings in a row the last time he played. Because of this lucky run, Paul thinks that Kings are the luckiest card. The dealer deals the first card to him. In a split second, he can see that it is a black card, but he is unsure if it is a King. What is the probability of the card being a King, given that it is a black card? Answer choices are in a percentage format, rounded to the nearest whole number. 8% 50% 67% 23 %

Paul went to a blackjack table at the casino. At the table, the dealer has Just shuffled a standard deck of 52 cards. Paul has had good luck at blackjack in the past, and he actually got three blackjacks with Kings in a row the last time he played. Because of this lucky run, Paul thinks that Kings are the luckiest card. The dealer deals the first card to him. In a split second, he can see that it is a black card, but he is unsure if it is a King. What is the probability of the card being a King, given that it is a black card? Answer choices are in a percentage format, rounded to the nearest whole number. 8% 50% 67% 23 %
Transcript text: Paul went to a blackjack table at the casino. At the table, the dealer has Just shuffled a standard deck of 52 cards. Paul has had good luck at blackjack in the past, and he actually got three blackjacks with Kings in a row the last time he played. Because of this lucky run, Paul thinks that Kings are the luckiest card. The dealer deals the first card to him. In a split second, he can see that it is a black card, but he is unsure if it is a King. What is the probability of the card being a King, given that it is a black card? Answer choices are in a percentage format, rounded to the nearest whole number. 8% 50% 67% 23 %
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Solution

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Solution Steps

Step 1: Identify the total number of cards and the number of black cards

A standard deck has 52 cards. Half of these cards are black (spades and clubs), so there are 26 black cards.

Step 2: Identify the number of black Kings

In a standard deck, there are 2 black Kings (one King of spades and one King of clubs).

Step 3: Calculate the probability of drawing a black King given that the card is black

The probability of drawing a black King given that the card is black is the number of black Kings divided by the total number of black cards: \[ \text{Probability} = \frac{\text{Number of black Kings}}{\text{Total number of black cards}} = \frac{2}{26} \]

Step 4: Convert the probability to a percentage

\[ \text{Probability (in percentage)} = \left( \frac{2}{26} \right) \times 100 \approx 7.69\% \]

Final Answer

8%

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