My Math Forum Possibilities of drawing balls?

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 December 9th, 2018, 08:51 PM #1 Newbie   Joined: Sep 2008 Posts: 7 Thanks: 0 Possibilities of drawing balls? I have a bag with 100 balls, 62 of them are red and the others 38 are white. if I take 4 of them at random, what are the probabilities of all of them being the white ones? Regards Last edited by sergio1971; December 9th, 2018 at 09:36 PM.
 December 9th, 2018, 09:56 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,382 Thanks: 1281 $\dfrac{\dbinom{62}{0}\dbinom{38}{4}}{\dbinom{100} {4}} = \dfrac{703}{37345}$
 December 10th, 2018, 01:32 PM #3 Global Moderator   Joined: May 2007 Posts: 6,710 Thanks: 675 Shorter formula $\frac{38\times 37\times 36\times 35}{100\times 99\times 98 \times 97}$
 January 4th, 2019, 11:42 PM #4 Newbie   Joined: Sep 2008 Posts: 7 Thanks: 0 thanks for your reply, in my previous post I should have pointed out that every time you take a ball, your notice its color and put in again in the bag so every time you reach for a ball there are 100 inside. can someone give me a correct answer ?. Thanks for your help
January 5th, 2019, 12:15 AM   #5
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Quote:
 Originally Posted by sergio1971 thanks for your reply, in my previous post I should have pointed out that every time you take a ball, your notice its color and put in again in the bag so every time you reach for a ball there are 100 inside. can someone give me a correct answer ?. Thanks for your help
The number of white balls you draw now becomes binomially distributed
with parameters

$n=4,~p=\dfrac{38}{100}$

$P[\text{all 4 chosen balls are white}]=\left(\dfrac{38}{100}\right)^4 = \dfrac{2085136}{100000000} = \dfrac{130321}{6250000}$

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