A "k 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. For a certain 4 out of 6 system, assume that on a rainy day each component has probability 0.7 of functioning and that on a non-rainy day each component has probability 0.9 of functioning. (a) What is the probability that the system functions on a rainy day? (b) What is the probability that the system functions on a non-rainy day? (c) Assume that the probability of rain tomorrow is 0.20. What is the probability that the system will function tomorrow?