Refer to Exercise 17 for the definition of a k out of n system. 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?
(a) On a rainy day, the number X of components that function is distributed Bin(6,0.7).
(b) On a nonrainy day, the number X of components that function is distributed Bin(6,0.9).
(c) Let R denote the event of a rainy day, and let F denote the event that the system functions. From part (a) we
know that P (F|R) = 0.7443, and from part (b) we know that P (F|Rc) = 0.9842.
(c) Let R denote the event of a rainy day, and let F denote the event that the system functions. From part (a) we
know that P (F|R) = 0.7443, and from part (b) we know that 
= 0.9842.
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