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 Post subject: red balls and white ballsPosted: Wed, 6 Jun 2012 23:00:33 UTC
 Senior Member

Joined: Mon, 30 Jan 2012 14:51:40 UTC
Posts: 54
In a box there are 5 red balls and 10 white balls. What is the probability that if you randomly select 5 balls, you will have 2 red balls and 3 white balls?

One way of finding the probability is

But can you find it using conditional probabilities?

for example:

R = Red ball selected event
W = White ball selected event

and five events so that

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 Post subject: Re: red balls and white ballsPosted: Thu, 7 Jun 2012 01:54:58 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7950
Location: Lexington, MA
Hello, cristi92b!

Quote:
In a box there are 5 red balls and 10 white balls.
What is the probability that if you randomly select 5 balls,
. . you will have 2 red balls and 3 white balls?

One way of finding the probability is:

But can you find it using conditional probabilities?

For example:

R = Red ball selected event
W = White ball selected event

and five events so that: .

I suppose you could . . . but who would want to?

First of all, "the five events" would have ten possible outcomes.
. .

Then for each one. we might go through this reasoning:

Consider

Hence: .

Then we go through the other nine cases
. . and we find that the probabilities are the same.

Therefore: .

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 Post subject: Re: red balls and white ballsPosted: Thu, 7 Jun 2012 11:33:24 UTC
 Senior Member

Joined: Mon, 30 Jan 2012 14:51:40 UTC
Posts: 54
Thank you!!!

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