Question

From a well shuffled pack of 52 cards, three cards are drawn one by one. The probability that the three cards are Jack, Queen and King respectively?

• A. \(\frac{11}{1105}\)
• B. \(\frac{8}{16575}\)
• C. \(\frac{27}{2197}\)
• D. \(\frac{27}{305}\)

Answer 1

The Correct Option is B

To determine the probability that three cards drawn sequentially from a standard deck of 52 cards are a Jack, Queen, and King respectively, we must calculate the probability of each event happening in order and then multiply these probabilities together. First, consider the number of ways to choose each card:

1. There are 4 Jacks in a deck of 52 cards. Therefore, the probability of drawing a Jack first is: \[ \frac{4}{52} = \frac{1}{13} \]
2. After drawing the Jack, there are 51 cards remaining, with 4 Queens among them. Thus, the probability of drawing a Queen next is: \[ \frac{4}{51} \]
3. After drawing a Queen, 50 cards remain, with 4 Kings among them. Thus, the probability of drawing a King as the third card is: \[ \frac{4}{50} = \frac{2}{25} \]

Multiplying these probabilities together gives the overall probability of drawing a Jack, then a Queen, then a King:

\[ \frac{1}{13} \times \frac{4}{51} \times \frac{2}{25} = \frac{8}{16575} \]

Thus, the correct probability that the three cards drawn are a Jack, Queen, and King in that specific order is \(\frac{8}{16575}\).