Emland Posts: 2,468, Reputation: 496 Ultra Member #1 May 3, 2007, 06:10 AM
How to solve this probability?
Okay - this isn't homework. I took statistics and let's just say although it wasn't pretty, I passed. My boss asked me to solve this probability question back when I was taking stats and I could never figure it out. He wants to know the probability for a bowling raffle he is in every year.

There are 3 fishbowls.

Inside each fishbowl there are 10 marbles.
3 marbles are black
7 marbles are white

What is the probability that if you pull 4 marbles from each jar that you will get 9 black marbles?

I told him about this site and that he might finally get an answer to this question that has been bugging him for a while. I hope someone knows!
 ebaines Posts: 12,132, Reputation: 1307 Expert #2 May 3, 2007, 07:22 AM
Originally Posted by Emland
Okay - this isn't homework. I took statistics and let's just say although it wasn't pretty, I passed. My boss asked me to solve this probability question back when I was taking stats and I could never figure it out. He wants to know the probability for a bowling raffle he is in every year.

There are 3 fishbowls.

Inside each fishbowl there are 10 marbles.
3 marbles are black
7 marbles are white

What is the probability that if you pull 4 marbles from each jar that you will get 9 black marbles?

I told him about this site and that he might finally get an answer to this question that has been bugging him for a while. I hope someone knows!
To get 9 black marbles, you must pull 3 blacks plus 1 white from each bowl. No other combination of choices will work. So, if we can find the probability of pulling 3 blacks and 1 white from a bowl, we cube that to get the probablility of doing it 3 times in a row.

The math is like this:

P(3 blacks + 1 white) = (3*2*1*7)/(10*9*8*7) * 4 = 0.0333

Note - the factor 4 is there because the white marble can show up in any one of the 4 picks.

So the probability of doing this feat 3 times in a row is 0.0333 ^ 3 = 0.000037037, or 1 out of 27,000.
 BRD4life Posts: 4, Reputation: 0 New Member #3 May 5, 2007, 05:28 PM
The one thing he failed to notice is the chance you could get 4 black marbles thus manking the proabailty slightly higher making it 0.001332:D :D :D
 Emland Posts: 2,468, Reputation: 496 Ultra Member #4 May 5, 2007, 05:30 PM
I don't understand BRD4life. There are only 3 black marbles per jar. How would you get 4 black marbles in one draw?
 anerd Posts: 1, Reputation: 1 New Member #5 Mar 4, 2011, 06:17 AM
But u can pick a 3 black and 1 white marble from a jar,So as there are 3 jars u will have 9 black marbles with you.
so probability to pick 3 black from a jar is 7/(10*3*7)
 ebaines Posts: 12,132, Reputation: 1307 Expert #6 Mar 4, 2011, 06:46 AM

anerd - you do realize that this question is almost 4 years old, and the correct answer was provided in post #2. I guess it's a good thing that at least we agree on what that answer is.

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