A k-out-of-n system functions provided that at least k of the n components function. Consider independently operating components, each of which functions (for the needed duration) with probability .96. 

a. In a 3-component system, what is the probability that exactly two components function?

b. What is the probability a 2-out-of-3 system works?

c. What is the probability a 3-out-of-5 system works?

d. What is the probability a 4-out-of-5 system works?

e. What does the component probability (previously .96) need to equal so that the 4-out-of-5 system will function with probability at least .9999?