# Math Help - Two Archers

1. ## Two Archers

We have two archers shooting at the target one after another. Probability of successful shot for the first archer is 0.4 and 0.5 for the second. They stop shooting after one of them has shot the target. What is the probability that the first archer shoots more arrows than the second?

Now, I'm not even sure how to start. It says that we should use this relation (for $x<1$):

$\sum_{n=0}^{\infty}x^{n}=\frac{1}{1-x}$.

I'm not asking for a complete solution. Just a few clues, please!

2. You are being asked to find the chance that the total number of shots is an odd number.

Spoiler:

=P(1 shot) = 0.4
+
P(3 shots) = (0.6*0.5)*0.4
+
P(5 shots) = (0.6*0.5)*(0.6*0.5)*0.4
+
...
...

You can recognise this as a geometric progression and use the formula you were given to find the total probability.