Achess player moves a knight from the location (3, 2) to (5, 1) on a chessboard. if the bottom-left square is labeled (1, 1), the translation made is . if the player moves the knight from (5, 1) to (6, 3), the translation made is

1)

When a  knight was moved from  (3, 2) to (5, 1) then the translation is:

         (x,y) → (x+2,y-1)

i.e. it  is moved 2 units to the right and 1 units down.

2)

If the knight is moved from (5, 1) to (6, 3).

The translation is:  

        (x,y) → (x+1,y+2)

i.e. it is moved 1 unit right and 2 units up.

This means that the knight is moved 2 units to the right and 1 units down.

( Since, when there is a change in the x-coordinate then it is either moved to the right or to the left and when there is a change in the y-coordinate then it is moved either up or down )

Then it is moved 1 unit right and 2 units up.

The real answer is:

1 square down, 2 squares right

2 squares up, 1 square right

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: