MHB How Did They Derive the Expression for P(Exactly One Match)?

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The discussion focuses on understanding how the expression for P(exactly one match) was derived. One participant suggests a straightforward approach by defining events A, B, and C for matching colors in specific boxes, calculating P(exactly one match) as P(A) + P(B) + P(C) = 1/2. Another participant acknowledges that this method is valid but seeks clarification on the original derivation. The conversation emphasizes the importance of clarity in probability expressions and invites further explanation. The inquiry remains open for additional insights on the derivation process.
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Hi guys, really simple question but...

http://img341.imageshack.us/img341/5447/ballsra.jpg

I'm not quite sure on how they ended up with the expression for P(exactly one match). I would have done it in a more straight forward way, simply define A: matching the colour red in the red box only. B: matching the colour blue in the blue box only and C: matching the colour white in the white box only.

So P(exactly one match) = P(A)+P(B)+P(C) = \frac{3}{6} = \frac{1}{2}

How exactly did they get their expression?

Thanks
 
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Usagi said:
So P(exactly one match) = P(A)+P(B)+P(C) = \frac{3}{6} = \frac{1}{2}
Yes, this also works.

Usagi said:
How exactly did they get their expression?
See https://driven2services.com/staging/mh/index.php?threads/788/.
 
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