Question

Suppose you have a deck of cards with the Jokers removed. If you draw 4 cards, what is the expected number of Kings you will draw?

Answer 1

1 times the probability you get 1 king plus
2 times the probability you get 2 plus
3 times the probability you get 3 plus
4 times the probability you get 4

Answer 2

may be a snappier way to do it, maybe not

Answer 3

So you would do 1(52 choose 3 times 4 choose 1) times( 2(52 choose 2) times(4 choose 2)) etc etc

Answer 4

yeah get \(\frac{4}{13}\)

Answer 5

oh no not 52 choose 3, etc but 48 choose 3

Answer 6

http://www.wolframalpha.com/input/?i=%28%284+choose+1%29%2848+choose+3%29%2B2%284+choose+2%29%2848+choose+2%29+%2B3%284+choose+3%29%2848+choose+1%29%2B4%29%2F%2852+choose+4%29

Answer 7

Oooh, okay, got it, thank you!

Answer 8

yw

Answer 9

i am willing to bet there is a snappy way to get such a simple answer, but i don't know it off the top of my head

Answer 10

Wait, are you sure this is right, just wondering because of the random four at the end of the top row! Should that be there?

Answer 11

yes

Answer 12

it is 4 times 4 choose 4

Answer 13

times 48 choose 0

Answer 14

which is all just 4