Question

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a face card for the second card drawn, if the first card, drawn without replacement, was a king? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Answer as a fraction = 11/51

Answer as a decimal = 0.2157

The decimal value is approximate.

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Step-by-step explanation:

The face cards are Jack, Queen, King.

We have 3 face cards for each suit, and 4 suits, giving 3*4 = 12 face cards out of a 52 card deck.

The first card is a king, which is not put back. This means have 12-1 = 11 face cards left out of 52-1 = 51 cards left.

The probability of getting another face card is 11/51 = 0.2157 approximately

This is about a 21.57% chance

Note: if the first card was put back, or replaced with an equal copy, then the answer would be 12/52 = 3/13 = 0.2308 = 23.08%

Answer 2

The probability of choosing a face card for the second card drawn if the first card was a king, drawn without replacement, is 11/663 or .0166.

Step-by-step explanation:

There are 52 cards and 12 of these are face cards.

The probability of drawing a king for the first card is the number of kings divided by the total number of cards:

• 4/52

The probability of drawing a face card after the first card was drawn without replacement is:

• 11/51

• When we take the king card out of the deck, we remove 1 from both the denominator and the numerator since it is also a face card.

Since these events are dependent (drawing without replacement), we can use this basic probability formula:

• 
  `P(A \cap B)=P(A) \cdot P(B)`

This formula tells us the probability of first drawing the king card, then drawing a face card afterward since 2 cards are being drawn. We must calculate the probability of both of these events occurring one after the other.

P(A) refers to the probability of getting a king on the first draw, 4/52, and P(B) refers to the probability of getting a face card on the second draw, 11/51.

Let's multiply these probabilities together.

• 
  `\displaystyle (4)/(52) \cdot (11)/(51) =(11)/(663)=.0166`

The probability of choosing a face card for the second card drawn, if the first card drawn without replacement was a king, is 11/663 or .0166.