Week 22 CAPT Problem - 9th 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 is the area of Square A?
   
   
2. What is the area of the whole board?
   
   
3. What percentage of the area of the whole board is the area of square A?
   What percentage of the time do you think a dart will hit square A?
   
   
4. What are chances it will land in the B square (but not in A)?(Hint - find the area of all of square B and subtract from it the area of square A. What percentage of the whole board is this area?)
   
   
5. What percentage of the time would you land in square A?
   What percentage of the time would you land in square B?
   What percentage of the time would you land in square C?
   What percentage of the time would you land in square D?
   If you played the game 100 times how much could you expect to win or lose?