Question

A standard deck of 52 playing cards contains

13 cards in each of 4 suits. What is the
appropriate probability that exactly three of
the cards are diamonds?
A) 1/4
B) 13/51
C) 3/13
D) 4/17

Answer 1

The probability that exactly three of the cards are diamonds is 13/51.The correct option is B.

Step-by-step explanation:

To find the probability that exactly three of the cards are diamonds, we need to consider the total number of ways to choose three diamonds out of the 13 diamonds in the deck, and divide it by the total number of ways to choose any three cards from the 52 cards in the deck.

The total number of ways to choose three diamonds out of the 13 diamonds is given by the combination formula: C(13, 3) = 286.

The total number of ways to choose any three cards from the 52 cards is given by C(52, 3) = 22,100.

Therefore, the probability that exactly three of the cards are diamonds is 286/22,100.

Answer: B) 13/51