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 Chikis July 12th, 2012 09:46 PM

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.

 MarkFL July 12th, 2012 10:04 PM

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:

$P(X)=3\cdot\frac{16\cdot15\cdot8}{36\cdot35\cdot34 }=\frac{16}{119}$

 Chikis July 13th, 2012 02:17 AM

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?

 MarkFL July 13th, 2012 09:06 AM

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.

 Chikis July 13th, 2012 10:42 AM

Re: The probability that: two are white and one is blue.

Alright! Thank you for the help.

 soroban July 13th, 2012 01:53 PM

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.

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

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

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

 M4mathematics July 25th, 2012 03:41 AM

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

 Denis July 25th, 2012 07:45 PM

Re: The probability that: two are white and one is blue.

 MarkFL July 25th, 2012 07:52 PM

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. :mrgreen:

 M4mathematics July 25th, 2012 08:32 PM

Re: The probability that: two are white and one is blue.

thanks, i remember next time.........

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