Question

HELP!!!!!
If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades?

Answer 1

there are 26 spades 2/26

Answer 2

7.69 but thats not one of my answers so Im doing something wrong

Answer 3

There are 13 spades out of 52 cards total. so what is the prob of drawing a spade on a first draw ?

Answer 4

oh I dont know why I was saying 26 13/52

Answer 5

25%

Answer 6

No.of ways drawing 6 cards out of 52 = 52C6 = 52!/(6!)*(46!)
No.of ways to select 2 spades = 13C2 =13!(11!)*2!

Answer 7

Now calculate the prob can u?

Answer 8

its just 13/52
now there are total 51 cards and 12 spades so So P(drawing spade on second draw) = 12/51 just keep on going like this till the 6 card is drawn

Answer 9

prob = (39C4*13C2)/(52C6)

Answer 10

39/4

Answer 11

sry binks i went some where wrong

Answer 12

13/52
12/51
11/50
10/49
9/48
8/47
@sidsiddhartha

Answer 13

@Muser can u help me?

Answer 14

P(drawing spade on first draw) = 13/52 I need to find out after drawing 6 cards the probability of drawing 2 spades

Answer 15

No, sorry. I was trying to work it out but I am definitely doing it incorrectly.

Answer 16

ok thanks

Answer 17

@amistre64 can u help please

Answer 18

@eliassaab can u help please???

Answer 19

(13/52)(8/47) ??? 2/47 = 0.0426 still not right

Answer 20

@texaschic101 please help!!!

Answer 21

If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades?

13*12*(52-13)*(52-14)*(52-15)*(52-16)
------------------------------------
52*51* 50* 49* 48* 47

but im sure thats not 100% accurate.

Answer 22

13 cards are spades, 39 are not spades

ss s's's's' (6 2) = 15 ways to arrange those?

1 5 10
1 6 15

(6 2) = 15 ways to arrange those

Answer 23

now im confused

Answer 24

13C2 * 39C4
------------
52C6

Answer 25

or
13P2 * 39P4
15 * -----------
52P6

Answer 26

http://www.wolframalpha.com/input/?i=%2813+choose+2%29+*+%2839+choose+4%29%2F%2852+choose+6%29

Answer 27

thanks now i see how to write it out

Answer 28

i believe this is called a hypergeometric probability distribution

but terminology never was a strong suit

Answer 29

i get the answer but still trying to figure out steps

Answer 30

consider, there are 39 cards that are NOT spades, there are 39*38*37*36 ways to pick 4 of them out of the deck

there are 13 cards that ARE spades, there are 13*12 ways to pick 2 of them out of the deck.

since this is without replacement, the number of cards in a deck reduce by 52*51*50*49*48*47; -1 card for each pull

there are 15 different ways to sort the pulls

Answer 31

thanks so much hope I can remember this lol

Answer 32

we had to determine the prob of poker hands last term .... it was horrible!! :)

Answer 33

i get the concept though

Answer 34

:)

Answer 35

hi

Answer 36

so whats the answer?

Answer 37

0.315 I believe