Originally Posted by

**HallsofIvy** Are you asking "how can I look at this problem and immediately know the aswer without doing any calculation?" I have no idea. But sitting down and doing some calculations might well show a pattern.

The first player will win on the first throw .05 of the time.

The second player will win on his first throw if the first player misses and he hits: (.95)(.15)

The first player will win on the second throw if the first player misses on the first try, second player misses, first player hits on second try: [tex](.95)(.85)(.05)

The second player will win on his second throw if the first player misses, second player misses, first player misses, second player hits: [tex](.95)(.85)(.95)(.15)

The first player will win on the third throw if they both miss twice and the he hits: (.95)(.85)(95)(.85)(.05)

The second player will win on the third throwif they bothiss twice, the first player misses, the second player hits: (.95)(.85)(.95)(.85)(.95)(.15)

So far for the first player we have

1: .05= ((.95)(.05))^0(.05)

2: .95(.85)(.05)= ((.95)(.85)^1)(.05)

3: .95(.85)(.95)(.85)(.05)= ((.95)(.85))^2(.05)

See a pattern?