What is the probability of hitting each target if it is assumed that a player’s throw will always hit the board? Hint: The probability of hitting each target

Question

 Width:20 Length: 12x+24 of all boards(rectangles). Target within board 1 measurements(rectangle): width 6x-3 length: 2x+4. target within board 2 measurements (circle): radius 6x. target within board 3 measurements (triangle):height 8x base:3x+6. 

Answer 1

The area of each board is 20(12x +24) = 20*12(x+2) = 240(x+2)

 

The area of the target in the first board is (6x-3)(2x+4)

 

Probability = {(6x-3)(2x+4)}/{20(12x+24)}

 

                =  {4(x-2)(x+2)/{240(x+2)}

                =  (x-2)/60

 

The area of the target in the second board is pi*(6x)*(6x) = pi*(36x^2)

 

Probability = pi*(36x^2)/ { 240(x+2)}

                = 3*pi*x^2/ {20(x+2)}

 

The area of the target in the third board is 1/2*(3x+6)*(8x) = 1/2*3*8*x(x+2) = 12*x*(x+2)

 

   Probability = 12*x*(x+2)/240(x+2) = x/20