Question

Suppose that 4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 4 are hearts?

Would the answer be 1/4, if I reduce it?

Thanks

Answer 1

With replacement:
(13/52)(13/52)(13/52)(13/52)
=(1/4)^4
= ?

Without replacement:
(13/52)(12/52)(11/52)(10/52)
= ?

Answer 2

C(13,4)/C(52/4)
= 715/270725
= 11/4165 or appr .002641

Nonetheless' second answer is not correct, should be
(13/52)(12/51)(11/50)(10/49)
which comes out to the same as my answer above

"drawing" cards usually means that you are holding the cards in your hand, thus they would not be returned after a draw.

Answer 3

Thanks for catching the denominator errors.

(Drawing can mean either with or without replacement; depends on the textbook, country, etc. so always good to clarify)