# Math Help - Probability Q

1. ## Probability Q

Here's a question from my homework that I'm stuck on:
Gunter tosses a die first, then Vlad. They repeat this until someone tosses a four, which means that person wins. Find the probability that Gunter wins, and the probability that Vlad wins.
For Gunter to win, wouldn't the probability just be 1/6, and for Vlad, the probability would be 5/6 * 1/6?

2. ## Re: Probability Q

Originally Posted by Otto45
Here's a question from my homework that I'm stuck on:
Gunter tosses a die first, then Vlad. They repeat this until someone tosses a four, which means that person wins. Find the probability that Gunter wins, and the probability that Vlad wins.
For Gunter to win, wouldn't the probability just be 1/6, and for Vlad, the probability would be 5/6 * 1/6?

Gunter can win on the first, third, fifth, etc turn.
The probability that Gunter wins on the ninth toss is ${\left( {\frac{5}{6}} \right)^8}\left( {\frac{1}{6}} \right)$.
Can you explain why?

What is this sum $\left( {\frac{1}{6}} \right)\sum\limits_{k = 0}^\infty {{{\left( {\frac{5}{6}} \right)}^{2k}}} =~?$

What does that sum represent?