See attachment for math work and answer.
All socks together: 13
Black socks: 3
Probability to pick out black socks: 3/13
After one pick out (You picked out a pair of black socks):
Probability to pick out black socks: 2/12
Multiply them:
2/12 * 3/13 = 1/26 ≈ 0,038
The general form for a line through two points (a,b) and (c,d) is
(c-a)(y-b)=(d-b)(x-a)
This is better than the slope forms because it works in the no slope case, as does the standard form.
If you haven't seen it before, it works because when (x,y)=(a,b) we get (c-a)(b-b)=(d-b)(a-a), both sides zero, and when (x,y)=(c,d) we get (c-a)(d-b)=(d-b)(c-a), clearly equal sides.
Here we have
(0 - -5)(y - 0) = (-9 - 0)(x - - 5)
5y = -9(x+5)
5y = -9x - 45
9x + 5y = -45
Ironically there are two standards for standard form; one with the constant alone on the right and one with the whole thing equal to zero. I like the constant alone.
Answer: 9x + 5y = -45
Check:
We check each point is on the line
(-5,0)
9(-5) + 5(0) = -45, good
(0, -9)
9(0) + 5(-9) = -45, good again
