Ak out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. Assume the components function independently of one another.
a. In a 3 out of 5 system, each component has probability 0.9 of functioning. What is the probability that the system will function?
b. In a 3 out of n system, in which each component has probability 0.9 of functioning, what is the smallest value of n needed so that the probability that the system functions is at least 0.90?