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

[Usagi]

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

 

[Evgeny.Makarov]

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

Yes, this also works.

How exactly did they get their expression?

See https://driven2services.com/staging/mh/index.php?threads/788/.