Question

What is the probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards?

Answer 1

Answer:      $\dfrac{11}{221}$

Step-by-step explanation:

We know that the total number of cards in a standard deck = 52

Then the number of ways to draw any two card = 52 x (52-1)

= 52 x 51 = 2652   [By Multiplicative principle]

Also , there are 12 face cards in a standard deck , so the number of ways to draw two face cards in succession = 12 x (12-1)

12 x 11= 132   [By Multiplicative principle]

Then, the probability of drawing 2 cards in succession (without replacement) from a standard deck and having them both be face cards would be

$\dfrac{\text{ Number of ways to draw 2 face cards}}{\text{Total number of ways to draw two cards}}$

$=\dfrac{132}{2652}=\dfrac{11}{221}$

Hence, the required probability is  $\dfrac{11}{221}$ .