Questions: Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a king and then, without replacement, another king? Express your answer as a fraction or a decimal number rounded to four decimal places.

$Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a king and then, without replacement, another king? Express your answer as a fraction or a decimal number rounded to four decimal places.$

Transcript text: Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a king and then, without replacement, another king? Express your answer as a fraction or a decimal number rounded to four decimal places.

Solution

Solution Steps

Step 1: Determine the probability of drawing the first king

A standard deck of 52 playing cards contains 4 kings. The probability of drawing a king on the first draw is: \[ P(\text{First King}) = \frac{4}{52} = \frac{1}{13}. \]

Step 2: Determine the probability of drawing the second king

After drawing the first king, there are now 51 cards left in the deck, and only 3 kings remain. The probability of drawing a second king is: \[ P(\text{Second King} \mid \text{First King}) = \frac{3}{51} = \frac{1}{17}. \]

Step 3: Calculate the combined probability

The combined probability of both events happening in sequence (drawing a king and then another king) is the product of the individual probabilities: \[ P(\text{First King and Second King}) = P(\text{First King}) \times P(\text{Second King} \mid \text{First King}) = \frac{1}{13} \times \frac{1}{17} = \frac{1}{221}. \]