Probability of an Event defined by two continuous random variables I'm having trouble solving this word problem.  I have the answer, but do not know how to get there.
An electronic gadget employs two integrated circuit chips: a signal processing chip and a power condition chip, which fail independently of each other.   The gadget fails to operate only upon the failure of either of the two IC chips (i.e. all other modalities of failure of the gadget can be ignored).  The time to failure of a chip is defined as the time interval between its manufacture and its failure, and is random (i.e. varies from chip to chip).  The time to failure for he signal processing chip, denoted by X, has an exponential distribution, having the probability density function:
$$
f_x(x) = ae^{-ax}u(x)\\
\text{where }  u(x) = \text{unit step function}\\
a = 10^{-4}/\text{hour}\\
f_y(y) = b e^{-by}u(y)\\
\text{where } b = 2 \cdot 10^{-4}/\text{hour}
$$
Question: Find the probability that, when a given sample of gadget fails, the failure is due to the power conditioning chip rather than the signal processing chip.
Answer: 2/3 

Hint: Let $Y$ be the random time taken for the power conditioning chip (PC) to fail and $X$ be the random time taken for the signal processing (SP) chip to fail. How do you denote the following event?$$\mathbb{P}[\{\text{Time required for SP chip to fail} > \text{Time required for PC chip to fail}\}]$$ If you figure out the above, you have your answer. 
