My Math Forum The probability that: two are white and one is blue.

 July 12th, 2012, 09:46 PM #1 Senior Member     Joined: Jan 2012 Posts: 725 Thanks: 7 The probability that: two are white and one is blue. A box contains identical balls of which 12 are red, 16 white and 8 blue. Three balls are drawn from the box one after the other without replacement. Find the probability that: two are white and one is blue. Please I need working and explaination.
 July 12th, 2012, 10:04 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: The probability that: two are white and one is blue. In the numerator, we will have the product $16\cdot15\cdot8$ and in the denominator $36\cdot35\cdot34$. There are 3 distinct ways to order the balls, hence: $P(X)=3\cdot\frac{16\cdot15\cdot8}{36\cdot35\cdot34 }=\frac{16}{119}$
 July 13th, 2012, 02:17 AM #3 Senior Member     Joined: Jan 2012 Posts: 725 Thanks: 7 Re: The probability that: two are white and one is blue. Yes you are right. That is the answer. Just give me a clue on how you know the number of orders, for example, this one is in this order P(wwb) + P(bww) + P(wbw) i.e 3 orders. How do you know the one that should be in two, three or six orders?
 July 13th, 2012, 09:06 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: The probability that: two are white and one is blue. The way I looked at it, there are three positions the one blue ball may occupy.
 July 13th, 2012, 10:42 AM #5 Senior Member     Joined: Jan 2012 Posts: 725 Thanks: 7 Re: The probability that: two are white and one is blue. Alright! Thank you for the help.
July 13th, 2012, 01:53 PM   #6
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Re: The probability that: two are white and one is blue.

Hello, Chikis!

Another approach . . .

Quote:
 A box contains identical balls of which 12 are red, 16 white and 8 blue. Three balls are drawn from the box one after the other without replacement. Find the probability that: two are white and one is blue.

$\text{Drawing 3 balls from the available 36 balls, there are: }\,{36\choose3} \,=\,7140\text{ possible outcomes.}$

$\text{To get two white and one blue, there are: }\,{16\choose2}{8\choose1} \,=\,960\text{ ways.}$

$\text{Therefore: }\:P(2W,\,1B) \;=\;\frac{960}{7140} \;=\;\frac{16}{119}$

 July 25th, 2012, 03:41 AM #7 Newbie   Joined: Jul 2012 From: India Posts: 8 Thanks: 0 Re: The probability that: two are white and one is blue. A box contains identical balls of which 12 are red, 16 white and 8 blue. Three balls are drawn from the box one after the other without replacement. Find the probability that: two are white and one is blue. possible combination WWB + WBW + BWW = 16/36 * 15/35 * 8/34 + 16/36 * 8/35 * 15/34 + 8/36 * 16/35 * 15/34 = 16/119
 July 25th, 2012, 07:45 PM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,146 Thanks: 1003 Re: The probability that: two are white and one is blue. Ahhh....I see...you're doing this to SNEAK IN your advertizing
July 25th, 2012, 07:52 PM   #9
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Re: The probability that: two are white and one is blue.

Quote:
 Originally Posted by M4mathematics A box...
I agree, you have posted the link to your site more than enough times on our forums.

It's great that you want to help, but please do so without spamming each post with a link. Thank you for your cooperation.

 July 25th, 2012, 08:32 PM #10 Newbie   Joined: Jul 2012 From: India Posts: 8 Thanks: 0 Re: The probability that: two are white and one is blue. thanks, i remember next time.........

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### 3 red, 4 white and 5 blue. 3 balls are drawn from box one after without replacemen. find probability that 3 are blue.

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