Alan

Green twice (with replacement):  p_g = (7/12)²

Red twice (with replacement):  p_r = (5/12)² 

Green twice or red twice (with replacement): p = p_g + p_r  

Green twice (without replacement):  p_g = (7/12)*(6/11)

Red twice (without replacement):    p_r = (5/12)*(4/11)

Green twice or red twice (without replacement):  p = p_g + p_r 

As follows:

See my reply at https://web2.0calc.com/questions/let-where-and-are-relatively-prime-positive-integers-find#r4 

The denominator is raised to the power 3, not 2.

As follows:

3(3)^2 + 3(3) + 12 means 3*3² + 3*3 + 12 or 3*9 + 9 + 12 or  27 + 9 + 12  or  48.

"A line in the coordinate plane has a slope of 4 and a distance of 1 unit from the origin. Find the area of the triangle determined by the line and the coordinate axes."

Triangle ABC is isosceles.  Picture a line perpendicular to AC and half way along, going from AC to B .  It will have a height given by sqrt(25² - 20²) by Pythagoras.  Hence the sin(ACB) = sqrt(25² - 20²)/25 = sqrt(5*45)/25 = 15/25 = 3/5

Because x - 1 is of first degree, f(x) must be one degree less than the degree of the polynomial on the RHS. i.e. f is of degree 3.

I simply wrote a simple brute force and ignorance program to find it!