Week 22 CAPT Problem - 10th Grade

Squares

The square board pictured above contains 3 other squares. There is a game that costs $1 to play. If you hit the A square you win $10. If you hit the B square you win $5. If you hit the C square you get $2. If you hit only in the D square you lose your $1 for that turn.

Suppose a dart hits the board at some random point :

1. What are the chances that you will land inside the A square ?
   
   
2. What are chances it will land in the B square (but not in A)?
   
   
3. What are the chances it will land in the C square (but not the A or B)?
   
   
4. If you played the game 100 times how much could you expect to win or lose? (Challenge Question)