Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace?

To find the probability of drawing two kings followed by an ace from a standard deck of 52 cards, we can break it down step by step.

Calculating the Probability

First, let's determine the total number of ways to draw the cards:

• There are 4 kings in the deck.
• After drawing the first king, there are 3 kings left.
• After drawing two kings, there are still 4 aces remaining in the deck.

Step-by-Step Breakdown

The probability of each draw is calculated as follows:

• Probability of drawing the first king: 4/52
• Probability of drawing the second king: 3/51
• Probability of drawing an ace after two kings: 4/50

Combining the Probabilities

Now, we multiply these probabilities together:

Probability = (4/52) × (3/51) × (4/50)

Calculating this gives:

Probability = (4 × 3 × 4) / (52 × 51 × 50)

Which simplifies to:

Probability = 48 / 132600

Finally, simplifying this fraction results in:

Probability = 1 / 2765

Final Result

The probability that the first two cards drawn are kings and the third card is an ace is 1/2765.