TITLE: What is the probability that the system is working?
QUESTION [2 upvotes]: A system consists of 10 devices.the system is working if atleast 8 devices are working.if each individual device is working with probability of 0.2,what is the probability that the system is working?

REPLY [2 votes]: HINT: It’s working if at most two devices have failed. Calculate the probability that no device has failed, the probability that exactly one device has failed, and the probability that exactly two devices have failed, and add them. Answers the following questions may help:

What is the probability that the first and third devices have failed and all other devices are working? How about the probability that the third and sixth devices have failed and all other devices are working?  
How many pairs of devices are there altogether?
{"set_name": "stack_exchange", "score": 2, "question_id": 548020}