Originally Posted by

**SpringFan25** This is almost identical to numerous other threads you have posted in the last few weeks. What exactly are you struggling with?

The CDF of the exponential distribution is:

$\displaystyle P(X\leq x)=1-e^{-\lambda x}$

so

$\displaystyle P(X>x)=e^{-\lambda x}$

So, the probability that the first component is alive after 1000 hours is $\displaystyle P(X_1>1000)=e^{-\lambda_1 *1000}$

similarly for X2, and X3 :

$\displaystyle P(X_2>1000)=e^{-\lambda_2 *1000}$

$\displaystyle P(X_3>1000)=e^{-\lambda_3 *1000}$

You want P(X1 and X2 and X3 alive after 1000 hours)