There is a box of 12 flares, four are selected at random. If the box contains four flares that don't work:

a- what is the probability that all four will not work?

b- What is the probability that, at most two will not work?

MY ANSWERS:

a = p(x=4)= C(4,4) x C(8,0)

/divided C(12,4)

24x1/19958400

0.0000012025 = 0.00012%

(that seems like a very low number for me)

b= x=equal or less 2

= C(4,2) x C(8,2) C(12,4) + C(4,1) x C(8,3) + (4,0) x (8,4)

/divided C(12,4)

= 403392/19958400 = 0.02021164 = 2%

That seems off to me as well...where am I going wrong????