Probability of the system 
A system consists of 2 processors and three peripherals. The lifetime of processors is an exponential random variable with mean 5. the life time of peripherals is an exponential random variable with mean 10. The system functions if at least one processor and two peripherals function. Assume the independence of the functions of the processors and peripherals.

*

*Find probability (P1) that the lifetime of a processor is longer than 4.

*Find probability (P1) that the lifetime of a peripheral is longer than 4.

*Find probability (PS) that the lifetime of the system is longer than 4.


In part 1 and 2, I use P(X>4) by exponential distribution
But in part 3, I dont know how to use this formula for system
p/s: I dont know what system is? that is confused me.
 A: 
The system functions if at least one processor and two peripherals
  function. Assume the independence of the functions of the processors
  and peripherals.

First you have to calculate, that at least two prozessors function. Let X be the random variable of the number of functioning processors. $p_1$ is the probability, that processor 1 is functioning. $p_2$ is the probability, that processor 2 is functioning.
Thus $P(X \geq 1)=p_1 \cdot (1-p_2)+(1-p_1)\cdot p_2 + p_1 \cdot p_2$
It is obvious, that $p_1=p_2$. I just have made the distinction to illustrate the structure of the calculation.
Let Y be the random variable of the number of functioning peripherals. $w_1$ is the probability, that peripheral 1 is functioning. $w_2$ is the probability, that peripheral 2 is functioning. $w_3$ is the probability, that peripheral 3 is functioning.
Thus $P(Y \geq 2)=w_1 \cdot w_2 \cdot (1-w_3)+w_1\cdot (1-w_2)\cdot w_3+(1-w_1)\cdot w_2 \cdot w_3+ w_1 \cdot w_2 \cdot w_3$
$w_1=w_2=w_3$
The probability, that the system functions is $P(X \geq 1)\cdot P(Y \geq 2)$
A: Man, it's been a long time since I've done this stuff.
For your question about what the system, it's defined in the sentence "The system functions if at least one processor and two peripherals function."
I suggest trying to break the problem down into parts that you can solve. Things that might be helpful for this: What is the relationship between independent probabilities? And how would you approach the question of "at least one processor" still functioning (ie. still being within its lifetime)?
