Question

If you draw three cards from a regular deck of 52 cards, what are the chances they are all hearts?

Answer 1

There are 13 hearts in a deck of 52 cards. So the probability of drawing a heart is 13/52 or 1/4. To find out what the chances of all three being hearts, we can multiply this probability:

$\sf\dfrac{13}{52}\times\dfrac{12}{51}\times\dfrac{11}{50}\rightarrow\boxed{\sf\dfrac{11}{850}}$

So the chances that all three cards will be hearts is 11/850.

Answer 2

Total number of cards = 52
Total number of hears = 13

Assuming the cards drawn are not replaced:
P(3 hearts) = (13/52)(12/51)(11/50) = 11/850

Answer: 11/850