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

A. The probability that both cards are fours is
`((1)/(221))`

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}} = (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}} = (3)/(51)`

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

`((4)/(52) ) *((3)/(51)) = (1)/(221)`

Hence, the probability that both cards are fours is
`((1)/(221))`