If you are dealt 4 cards from a shuffled deck of 52​ cards, find the probability that all 4 cards are diamonds.

Question

f you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are diamonds.

Answer 1

Hi Gina, there are several ways to solve this problem.

 

Probability of drawing a diamond:

 

There are 13 diamonds in a deck of 52 cards. The probability of drawing 1 diamond is 13/52.

 

Now there are only 12 diamonds and 51 cards. The probability of drawing 1 diamond is 12/51.

 

The third and forth diamonds follow the pattern and are 11/50 for the third diamond and 10/49 for the forth diamond.

 

The probability of drawing 4 diamonds is: 13/52 * 12/51 * 11/50 * 10/ 49, or 715/270725 (if my multiplication and division is correct.)

 

Using combinations:

 

Ways to draw any 4 cards:

 

Number of combinations of drawing 4 cards from 52: 52C4, or 270725.

 

ways to draw any 4 diamonds from 13 diamonds:

 

Number of combinations of drawing 4 cards from 13: 13C4, or 715

 

Probability of drawing 4 diamonds from 52 cards: 715/270725.

 

Questions?

Answer 2

Never mind. My solution was incorrect