NASA is planning a deep space probe involving extensive scientific experimentation. The guidance system for the space vehicle is obviously critical. The system is comprised of six independent components, each of which must work as engineered in order for the overall system to function properly. If each component has a 10% chance of failing,
a. How likely is it that two or more of the components will fail during the fight?
b. There is less than a 1% chance that ___ or more components will fail during the fight?
c. How likely is it that the system (that is, all 6 components) will work properly?
d. Suppose NASA plans to include a backup unit for each of the 6 components. Tests show that, in each case, either the backup or the primary component will function properly 95% of the time (that is, the chance of both the backup and the primary failing is only 5%). What is the probability that the system will function properly during the mission?