An experiment consists of dealing 7 cards from a standard 52-card deck. What is the probability of being dealt 7 hearts?

Question

An experiment consists of dealing 7 cards from a standard 52-card deck. What is the probability of being dealt 7 hearts?

Answer 1

There are 13 heart cards and 52 total cards.  Thus, ...

 

(13/52)(12/51)(11/50)(10/49)(9/48)(8/47)(7/46)(6/45)(5/44)(4/43)(3/42)(2/41)(1/40)=1.5747695e-12

 

In which case, there is a 1.5747695e-10% chance that you are dealt 7 hearts from a 52 card deck.

Answer 2

The probability that the first card is a heart is 13/52

For the second card it is 12/51 (There are only 51 cards and only 12 of them are in the heart suit.)

For the third card it is 11/50

4th card 10/49

5th card 9/48

6th card 8/47

7th card 7/46

 

The total probability of all of these events occurring is the product of each individual probability.

 

So, the answer is (13 * 12 * 11 * 10 * 9 * 8 * 7) / (52 * 51 * 50 * 49 * 48 * 47 * 46)

 

which equals exactly 33 / 2,572,780 or roughly 1 chance in about 77,963 

Answer 3

Kelsey,

 

You have 13 hearts.

one being heart is 13/52 = 1/4

two being heart is (13/52)(12/51)

three being heart (13/52(12/51)(11/50)

four being heart (13/52(12/51)(11/50)(10/49)

five being heart (13/52(12/51)(11/50)(10/49)(9/48)

six being heart (13/52(12/51)(11/50)(10/49)(9/48)(8/47)

being heart (13/52(12/51)(11/50)(10/49)(9/48)(8/47)(7/46)

It is easier with the formula. You would get nice looking factorial.

13 choose 7 over 52 choose 7 <=> (13!/7!)/(52!/7!)

I hope this helps