An urn has 3 red balls 4 white balls and 2 black balls What is the probability that the first red ball comes before the first white ball comes? Also, there is replacement/repetition.

So i understand you probably need to get the probability of the red ball and then the probability of the white ball but how do you answer specifically the last question? Thank You

  • $\begingroup$ What's the probability of drawing a red ball? A black ball then a red ball? A black ball then a black ball then a red ball? ... $\endgroup$ – Matthew Gunn Dec 11 '15 at 1:54
  • $\begingroup$ Is the drawing process endless? $\endgroup$ – pe-pe-rry Dec 11 '15 at 2:08
  • $\begingroup$ Yes... possibly. $\endgroup$ – David G. Stork Dec 11 '15 at 2:09
  • $\begingroup$ Yes it is, forgot to include that information $\endgroup$ – Ben P Dec 11 '15 at 2:17

Drawing a black ball has no bearing on the probability that the next white/red ball drawn will be white or red, so long as no white/red balls have been chosen already, and regardless if the process is reset after each ball is drawn (ball is put back into urn). So you can simply ignore any instances of black balls being drawn. The chance of a red ball being drawn before a white ball is then just $3/7$ - exactly the same as it would be if there were no black balls in the urn.


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