Question

when draw a 13 card hand from a 52 deck card, what is the probability of having 6 cards from the same suit

Answer 1

help please?

Answer 2

5.5%

Answer 3

5.59

Answer 4

really?

Answer 5

52-13= 39

Answer 6

binompdf(13,.25,6) = 5.59224

Answer 7

.0559 but 5.59 percent

Answer 8

there are \(\binom{52}{13}\) way to select your 13 card
lets do it for one suit, say \(\diamondsuit\)
out of the 13 you select, there are \(\binom{13}{6}\) ways to get 6 diamonds, and \(\binom{39}{7}\) ways to select the other 7 cards

Answer 9

I think she was asking the probability

Answer 10

so for all four suits my guess is
\[\frac{4\binom{13}{6}\binom{39}{7}}{\binom{52}{13}}\]

Answer 11

oh idk then

Answer 12

it could be binompdf(13,.25,6) but i have no idea what that means or how to compute it

Answer 13

i get a different number
http://www.wolframalpha.com/input/?i= \frac{4\binom{13}{6}*\binom{39}{7}}{\binom{52}{13}}

Answer 14

Can you guys show me the entire procedure?

Answer 15

i wrote out the method above and i think it is
\[\frac{4\binom{13}{6}\binom{39}{7}}{\binom{52}{13}}\]
each of these numbers in the fraction are large and a pain to compute, i would use a calculator

Answer 16

Is (13 6) the same as 13 nCr 6?

Answer 17

yes

Answer 18

I believe it is 5.59% Go onto a ti-83/84 and hit 2nd VARS and go down to binompdf
Then the first number is the number of trials 13
second number is the initial percent .25
third is howmany you want to succeed 6

Answer 19

http://www.wolframalpha.com/input/?i=4%2813+choose+6%29*%2839+choose+7%29%2F%2852+choose+13%29

Answer 20

@ryderpeppler i see what you are doing, but these are not bernoulli trials, you can't use the binomial distribution

Answer 21

what you are calculating is the probability of getting exactly 6 successes out of 13 trials, where the probability of each success is .25
but you cannot use that here, because the trials are not independent

Answer 22

ah so the method I used doesnt account for there being less cards and a lower probability after the first drawn card?

Answer 23

Then why is my percentage lower than yours?

Answer 24

right

Answer 25

Thank you so much!

Answer 26

Well it'll either be 16.6 (17 with sig figs) or 5.59 (6 with sig figs) percent

Answer 27

this is an entirely different question
you do not have only two possible outcomes, "success or failure"

Answer 28

also there are four different suits to choose from