# The Ultimate Target

## Idea

Douglas is playing a new shooting game. The object of the game is to win. To do so, he must get the most points on 3 different levels. The points will vary dependent upon where he hits on the target. He will still move on to the next round even if he misses. If he hits the bullseye he will get bonus points. He gets 1 shot per round.

• The probability of him hitting on the 1st level is 40%
• The probability of him hitting on the 2nd level is 20%
• The probability of him hitting on the final level is 30%
• The probability of him hitting on the first try is .6
• The probability of him hitting the bullseye is .2

## Assumptions

• There are different distances on different levels
• It is a working weapon
• The game is not tampered with

## Situations

1. What is the probability of him hitting on the 1st try and hitting the bullseye? 12%
2. What is the probability of him hitting the target on the first level or missing on the second level? 60%
3. Given that he makes it to the final round, what is the probability of him hitting the bullseye on this level? 6%