Cdf of system, exponential distribution

These 3 components function independently of each other. Suppose the i-th component has a lifetime that is exponentially distributed with λ1, λ2, and λ3 (given values)

X=time at which system fails..

the system:

http://i140.photobucket.com/albums/r...Untitled-2.jpg

okay so im trying to find the cdf F(x)=P(X<=x)

first... Ai=Ai(x)={Xi>=x}

I tried to find the cdf for component 1 and 2 and did A(x)={X>=x}=A1(x)*A2(x) and found the probability of A(x) to get the cdf equal to **1-e^(-(λ1+λ2)*x)**

and for component 2 and 3 i got a cdf of **(1-e^(-λ2*x))*(1-e^(-λ3*x))**

when the question asks cdf F(x)=P(X<=x) so I add the two cdfs I got or is the answer to that problem the cdf for component 1 and 2? hope this makes sense...