This problem can be thought of as drawing one marble and then a 2nd marble, without replacement:



P(first is red) = 18/(18+30) = 18/48

P(2nd is red) = 17/(17+30) = 17/47



P(both are red) = (18/48)*(17/47) = 306/2256 or approx. 0.1356 (13.6%)



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If you compute it assuming both are drawn at the same time, you get:

  C(18,2) / C(48,2) = ((18*17)/2) / ((48*47)/2) = (18*17)/ (48*47) = 306/2256, as above.



Where C(n,r) = n!/((n-r)!r!)

 

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