2
$\begingroup$

So the problem is in Tanis & Hogg, Probability and Statistical inference section 1.5 Independence of Events.

An Urn contains five balls, one marked WIN and four marked LOSE. You and another player take turns selecting a ball at random from the urn, one at a time. The first person to select the WIN ball is the winner. If you draw first, find the probability that you will win if the sampling is done with replacement.

I can't see why the probability isn't $\displaystyle\frac{1}{5}$. The book states it is $\displaystyle\sum_{k=0}^\infty(\displaystyle\frac{1}{5}\times\displaystyle\frac{4}{5}2k)$

Thanks!

  • 0
    The probability is $\frac{1}{5}$ that you win on the _first_ turn. But if neither you nor your opponent win on your first turns, you might still win on the _second_ turn, etc.2012-06-07

5 Answers 5