I am reading the following problem:
There is a political discussion group consisting of $5$ democrats, $6$ republicans, and $4$ independents. Suppose that two group members are randomly selected in succession to attend a political convention. Find the probability of selecting no Independents
My solution was:
Probability of both selected are independents = $$\frac{4}{15}\cdot \frac{3}{14} =\frac{4}{70}$$
Probability of selecting no independents = $1$ - Probability of both selected are independents = $$ 1 - \frac{4}{70} = \frac{66}{70}$$
According to the solution this is wrong but why? Isnt the select none the complement of select $2$ in a sequence?
Update I am interested in understanding the falacy I am doing in the logic