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?
a = p(x=4)= C(4,4) x C(8,0)
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)
= 403392/19958400 = 0.02021164 = 2%
That seems off to me as well...where am I going wrong????