Question

Two cards are chosen from a standard deck of 52 playing cards without replacement. What is the probability that both cards are fours?

A. 1/221
B.30/221
C.1/69
D.3/676

Answer 1

Answer:

A. The probability that both cards are fours is $(\frac{1}{221})$

Step-by-step explanation:

The total number of cards in the deck = 52

The total 4 in the given deck =  4 ( Spade, club, hearts, diamond)

Now, if a first card is chosen, the probability of it  being a 4 is:

$\textrm{P (Choosing a 4)} = \frac{\textrm{Total number of 4 in the deck}}{\textrm{Total Cards in the deck}} = \frac{4}{52}$

Now, if the picked card is  NOT REPLACED:

Total Cards in the deck = 52 -1 = 51

$\textrm{P (Choosing a 4)} = \frac{\textrm{Total number of 4 in the deck}}{\textrm{Total Cards in the deck}} = \frac{3}{51}$

So, the combined probability of picking two fours from a givne deck WITHOUT REPLACEMENT is:

$(\frac{4}{52} ) \times(\frac{3}{51}) = \frac{1}{221}$

Hence, the probability that both cards are fours is $(\frac{1}{221})$